MIC Ferrite Phase Shifter
MIC Ferrite Phase Shifter
A MIC ferrite phase shifter is a microwave integrated circuit component that uses the electromagnetic properties of ferrite material to control the phase of a microwave signal. In a conventional transmission line, the phase accumulated by a signal is mainly determined by its frequency, physical length, and propagation characteristics of the medium. In a ferrite-based MIC phase shifter, however, the propagation characteristics can be electrically controlled by applying a static magnetic field to the ferrite substrate. The magnetic field changes the magnetization state of the ferrite, which changes the effective electromagnetic properties experienced by the microwave signal and consequently changes its propagation constant. Since the physical length of the microstrip line can remain fixed while its propagation constant is varied, the phase of the microwave signal can be controlled electrically without mechanically changing the transmission-line length.
The basic structure of a MIC ferrite phase shifter consists of a ferrite substrate with a microstrip transmission line formed on it. The microwave signal propagates along the microstrip line while interacting with the ferrite material beneath the conductor. A static magnetic field \(H_0\) is applied to the ferrite to establish a particular magnetization state. Depending on the magnitude and direction of this applied magnetic field, the magnetization vector \(M\) of the ferrite can be changed. Because the microwave propagation constant depends on the effective magnetic properties of the ferrite, changing the magnetization changes the propagation constant of the microstrip transmission line. The phase accumulated by the microwave signal over a fixed physical length is therefore changed electrically.
The phase accumulated along a transmission line is related to its propagation constant and physical length according to
\[ \phi = \beta l \]
where \(\phi\) is the phase accumulated by the microwave signal, \(\beta\) is the propagation constant of the transmission line, and \(l\) is the physical length of the microstrip line. In a MIC ferrite phase shifter, the physical length \(l\) can be kept constant while the propagation constant \(\beta\) is changed through the magnetization of the ferrite. Therefore, the phase shift can be controlled by electrically controlling the magnetic state of the ferrite rather than by physically altering the transmission path.
The static magnetic field \(H_0\) is therefore an important control quantity in a ferrite phase shifter. It establishes the magnetization of the ferrite and determines the magnetic environment through which the microwave signal propagates. The magnetization vector \(M\) can be altered either by changing the magnitude of the applied magnetic field or by changing its direction. These changes modify the interaction between the ferrite and the RF electromagnetic field associated with the microstrip transmission line. As a result, different values of propagation constant can be obtained for different magnetic states, producing different amounts of phase shift for the same physical transmission-line length.
The electrical control of phase shift provides an important practical advantage. Because the phase is changed by controlling the magnetic properties of the ferrite, there is no need to physically move a transmission-line section or introduce a mechanically adjustable structure. This allows ferrite MIC phase shifters to be designed as low-cost, compact, and highly reliable microwave components. Their microstrip construction also makes them suitable for integration with other microwave circuits, while electrical control allows the phase state to be changed conveniently according to the requirements of the system.
1. Types of MIC Ferrite Phase Shifters
MIC ferrite phase shifters can be broadly classified according to the method used to control the magnetization of the ferrite. The two principal types are analog-controlled ferrite phase shifters and digital-controlled ferrite phase shifters. In an analog phase shifter, the phase is controlled continuously by varying the magnitude or direction of the magnetization. In a digital phase shifter, the ferrite is switched between selected magnetic states so that discrete phase-shift values are obtained. The distinction between these two types is therefore based mainly on how the magnetization state, and consequently the propagation constant, is controlled.
A. Analog Control
An analog ferrite phase shifter provides continuous control of phase by continuously changing the magnetic state of the ferrite substrate. A static magnetic field \(H_0\) is applied to the ferrite, and the resulting magnetization vector \(M\) determines the magnetic response experienced by the microwave signal. By varying the applied magnetic field, the magnitude of magnetization can be changed, or the direction of the magnetization vector can be altered. These changes modify the effective permeability of the ferrite and therefore modify the propagation constant of the microstrip transmission line.
The important feature of analog control is that the phase does not have to be restricted to a small number of predefined values. When the magnitude of the magnetization is varied continuously, the electromagnetic interaction between the RF field and ferrite also changes continuously. Consequently, the propagation constant varies with the magnetic state, and the phase accumulated over the fixed microstrip length changes continuously. This provides a continuously adjustable phase shift and makes analog ferrite phase shifters useful when a microwave system requires fine electrical control of signal phase.
The direction of the magnetization vector can also be used as an analog control parameter. Changing the orientation of \(M\) changes the relationship between the ferrite magnetization and the RF magnetic field associated with the microstrip line. Since the effective magnetic response depends on this relationship, different magnetization directions can produce different propagation constants. Thus, both the magnitude and the direction of magnetization can be used as mechanisms for controlling the phase response of the device.
B. Digital Control
A digital ferrite phase shifter operates by switching the ferrite between predefined magnetization states rather than continuously varying the magnetic state. Each magnetization state corresponds to a particular propagation condition and therefore produces a particular phase shift. The magnetic state is controlled electrically, typically by applying a current pulse through a suitable conductor associated with the ferrite substrate. When the ferrite changes from one magnetic state to another, the propagation constant changes and the phase of the microwave signal changes accordingly.
Digital control is particularly useful when a microwave system requires a fixed set of accurately defined phase states. Instead of continuously controlling the magnetic field, the phase shifter can be designed with a specified number of digital states. A phase shifter with more bits can provide a larger number of available phase states and therefore a finer phase resolution. The digital approach also makes it possible to implement compact electronically controlled phase-shifter networks in which different sections are independently actuated.
I. High-Remanence Ferrite
Digital ferrite phase shifters use high-remanence ferrite materials so that the selected magnetic state can be retained after the externally applied magnetizing current is reduced to zero. The term remanence describes the residual magnetic induction that remains in a magnetic material after the externally applied magnetizing field or current has been removed. This property is essential for latching operation because the ferrite can retain its selected magnetization state without requiring continuous application of the magnetizing current.
The magnetic behavior of a ferrite can be represented using its B-H curve, where \(B\) represents magnetic induction and \(H\) represents the applied magnetic field. When the magnetizing field is reduced after the material has been magnetized, the magnetic induction does not necessarily return to zero. The remaining magnetic induction represents the remanent magnetic state of the material. A high-remanence ferrite therefore provides a suitable material basis for digital phase shifters because the desired magnetization state can be retained after the control pulse has ended.
High remanence makes it possible to use a latching phase-shifter operation. Instead of continuously supplying power to maintain the magnetic state, a sufficiently strong current pulse can establish the required magnetization, after which the ferrite retains that state. A subsequent control pulse can then be used to change the magnetization to another state. This provides an efficient method of electrically switching the phase response of the microwave transmission line.
II. Latching Operation
In a latching digital ferrite phase shifter, the ferrite substrate is magnetized using a current pulse of sufficient amplitude. The current is passed through a single-turn wire that threads the ferrite substrate. The magnetic field produced by this current changes the magnetization of the ferrite. By selecting the magnitude and direction of the current pulse appropriately, the ferrite can be driven into the required magnetic state.
Once the magnetizing current pulse is reduced to zero, a high-remanence ferrite can retain the magnetization produced by the pulse. The selected state therefore remains stored in the ferrite without the need for a continuous DC magnetizing current. This behavior is known as latching. The phase shifter consequently remains in the selected phase state until another suitable current pulse is applied to change the magnetization.
The direction of the DC magnetic field can also be reversed through the control current. Reversing the magnetization direction changes the magnetic state of the ferrite and consequently changes the propagation characteristics of the microstrip line. In this way, electrical current pulses can be used to switch the phase shifter between discrete phase states. The microwave signal itself continues to propagate through the same physical microstrip structure, while its phase response is changed by the magnetic state of the ferrite.
The latching principle is especially valuable for digital microwave systems because the control circuit only needs to provide the appropriate pulse when a change of state is required. After switching, the ferrite retains its magnetic state until another control operation occurs. This gives the digital phase shifter a stable stored phase state while keeping the physical structure compact and electrically controllable.
III. Digital Phase-Shift Resolution
The phase resolution of a digital phase shifter is determined by the number of available digital states. If a digital phase shifter has \(n\) bits, it provides \(2^n\) distinct phase states when all combinations of the digital control bits are used. The smallest controllable phase increment is called the least significant bit (LSB) phase shift. For an ideal \(n\)-bit phase shifter covering a full \(360^\circ\) phase range, the LSB phase shift is given by
\[ \Delta\phi_{\text{LSB}}=\frac{360^\circ}{2^n} \]
This relationship shows that increasing the number of bits increases the number of available phase states and reduces the smallest phase increment. For example, a digital phase shifter with a greater number of bits can provide finer phase resolution because the total \(360^\circ\) phase range is divided into a larger number of discrete steps. The number of bits therefore directly determines the theoretical phase resolution of the digital phase-shifter system.
A practical digital phase shifter can be constructed using several separately actuated sections, with each section contributing a particular phase shift. Each section is controlled independently so that different combinations of sections can be selected. The phase contribution of the individual sections is arranged according to the binary weighting required for the selected number of bits. By combining the phase shifts produced by the individual sections, the complete digital phase-shifting range can be obtained.
For a 3-bit digital ferrite phase shifter, three independently controlled sections can be designed to provide phase shifts of \(180^\circ\), \(90^\circ\), and \(45^\circ\), respectively. These three sections correspond to the binary-weighted phase contributions of the three control bits. Different combinations of the sections produce different total phase shifts. The sections can be cascaded within a single housing so that they operate together as one integrated digital phase shifter.
The use of \(180^\circ\), \(90^\circ\), and \(45^\circ\) sections illustrates how a digital ferrite phase shifter can obtain multiple discrete phase states from several individually controlled magnetic sections. Each section is switched between its available magnetic states, and the resulting phase contributions combine along the microwave signal path. The complete device can therefore provide digitally selectable phase control while maintaining a fixed physical microwave transmission path.
Reciprocal Ferrite Phase Shifter and Phase-Constant Analysis
A reciprocal ferrite phase shifter uses the dependence of the microwave propagation constant on the magnetization state of a ferrite substrate. The microwave signal propagates along a microstrip transmission line formed on the ferrite material, while an externally applied static magnetic field establishes the magnetization of the ferrite. By changing the direction of magnetization, the effective permeability experienced by the RF field changes. Since the propagation constant depends on the effective permeability, different magnetization directions produce different phase constants and therefore different phase shifts for the same physical length of microstrip line.
In the reciprocal configuration, the ferrite is arranged so that the interaction responsible for the phase shift remains essentially reciprocal. Two important magnetization orientations are considered: magnetization perpendicular to the microstrip line and magnetization parallel to the microstrip line. These two orientations produce significantly different interactions between the ferrite and the RF magnetic field. The perpendicular orientation produces very small interaction, whereas the parallel orientation produces maximum interaction. This difference in effective magnetic response is the basis for obtaining two different propagation constants and hence a controllable phase shift.
2. Reciprocal Phase Shifters
The operation of a reciprocal ferrite phase shifter can be understood by examining how the effective RF permeability changes when the direction of ferrite magnetization is changed. The ferrite substrate is first magnetized to saturation in one direction and then can be switched to another direction. Because the RF magnetic field produced by the microstrip line has a particular orientation relative to the ferrite magnetization, the electromagnetic interaction is different for different magnetization states. The resulting change in effective permeability produces a corresponding change in the propagation constant of the microwave signal.
A. Perpendicular Magnetization
Consider the ferrite substrate magnetized to saturation in a direction perpendicular to the microstrip line. In this configuration, the orientation of the static magnetization is such that the interaction between the ferrite magnetization and the RF magnetic field associated with the microstrip transmission line is very small. As a result, the ferrite produces only a very small change in the effective magnetic environment experienced by the propagating microwave signal.
Because the interaction is very small, the effective RF relative permeability can be approximated as unity. Thus, for the perpendicular magnetization state, the effective permeability is written as
\[ \mu_{r\mathrm{eff}}\approx1 \]
This approximation means that, from the viewpoint of the RF wave, the magnetic behavior of the ferrite substrate contributes very little additional loading in this particular magnetization orientation. The propagation constant in this state is therefore determined primarily by the dielectric properties and the geometry of the microstrip structure, with the magnetic contribution being approximately equivalent to that of a non-magnetic medium.
The perpendicular magnetization state is consequently useful as one of the reference states of a reciprocal ferrite phase shifter. When the ferrite is switched from this state to a direction that produces stronger RF interaction, the effective permeability changes. The corresponding propagation constant also changes, allowing the phase accumulated along the fixed microstrip line to be controlled electrically.
B. Parallel Magnetization
When the ferrite substrate is magnetized to saturation in a direction parallel to the microstrip line, the interaction between the ferrite and the RF magnetic field becomes much stronger. In this orientation, the RF field interacts significantly with the magnetized ferrite, so the effective permeability seen by the microwave signal is no longer approximately unity. This produces a substantial change in the propagation characteristics of the microstrip line.
The effective RF relative permeability for the parallel magnetization state is described using the components of the ferrite permeability tensor. The effective permeability is given by
\[ \mu_{r\mathrm{eff}}=\frac{\mu^2-K^2}{\mu} \]
Here, \(\mu\) represents the diagonal component of the ferrite permeability response and \(K\) represents the off-diagonal or gyrotropic component associated with the magnetized ferrite. These quantities arise because a magnetized ferrite is not electromagnetically equivalent to an ordinary isotropic magnetic material. Its magnetic response depends on the direction of the applied RF magnetic field relative to the static magnetization.
The permeability parameter \(\mu\) is related to the magnetic flux density \(B\) and magnetic field intensity \(H\) and can be expressed as
\[ \mu=\frac{B}{H} \]
The parameter \(K\) represents the gyrotropic contribution to the permeability tensor and is related to the magnetization and operating angular frequency. In the supplied formulation, it is written as
\[ K=\frac{\gamma 4\pi M}{\omega} \]
where \(M\) is the magnetic dipole moment per unit volume, \(\gamma\) is the gyromagnetic ratio, and \(\omega\) is the angular frequency of the microwave signal. The presence of \(K\) is important because it represents the directional magnetic response produced by the magnetized ferrite. Consequently, the effective permeability for the parallel configuration differs from the simple permeability of an unmagnetized magnetic material.
The important physical difference between the two magnetization states is therefore the strength of interaction with the RF magnetic field. For perpendicular magnetization, this interaction is very small and \(\mu_{r\mathrm{eff}}\) is approximately unity. For parallel magnetization, the interaction is maximum and the effective permeability must be described using the ferrite's gyrotropic permeability response. This difference provides the magnetic mechanism required for phase shifting.
C. Effective Permeability and Magnetic Response
The effective permeability of the ferrite also depends on the strength of the applied magnetic field and the operating frequency. Under the small applied-field condition and for frequencies satisfying \(\omega>\omega_m\), the effective relative permeability can be approximated by
\[ \mu_{r\mathrm{eff}}\approx1-\left(\frac{\omega_m}{\omega}\right)^2 \]
This expression shows that the magnetic response depends strongly on the ratio between the ferrite magnetization frequency \(\omega_m\) and the microwave angular frequency \(\omega\). When the operating frequency is sufficiently higher than \(\omega_m\), the ratio \(\omega_m/\omega\) becomes smaller and the effective permeability approaches unity. As the operating frequency approaches the characteristic magnetic frequency, however, the magnetic response becomes increasingly significant.
The quantity \(\omega_m\) is associated with the saturation magnetization of the ferrite and is defined by
\[ \omega_m=\gamma 4\pi M_s \]
where \(M_s\) is the saturation magnetization of the ferrite and \(\gamma\) is the gyromagnetic ratio. The quantity \(4\pi M_s\) represents the ferrite magnetization in the commonly used cgs-based formulation. The gyromagnetic ratio specifies the relationship between magnetic-field strength and the corresponding magnetic precession frequency of the ferrite magnetization.
For the ferrite material considered in the supplied formulation, the gyromagnetic ratio is approximately
\[ g=2.8\ \text{MHz/Oe} \]
The value of the gyromagnetic ratio determines the relationship between the magnetic properties of the ferrite and its electromagnetic response at microwave frequencies. Therefore, the material parameters of the ferrite, particularly its saturation magnetization, directly influence the frequency-dependent effective permeability and consequently the phase-shifting behavior of the device.
An important limitation occurs when the operating angular frequency approaches \(\omega_m\). In this region, the magnetic response becomes strong and the assumption of negligible magnetic loss is no longer valid. Therefore, when \(\omega\) approaches \(\omega_m\), magnetic loss cannot be neglected and the simple approximate expression for effective permeability must be modified to account for the lossy magnetic response of the ferrite.
Thus, the effective permeability is not simply a constant material property in a magnetized ferrite phase shifter. It depends on the magnetization state, operating frequency, and magnetic-field conditions. This frequency-dependent and magnetization-dependent permeability is what allows the ferrite substrate to control the propagation characteristics of the microwave signal.
D. Propagation Constant of the TEM Mode
The microwave signal propagating along the microstrip transmission line can be treated approximately as a TEM mode for the purpose of analyzing its propagation constant. The propagation constant determines how rapidly the phase of the microwave signal changes as it travels along the transmission line. For a ferrite-loaded structure, the propagation constant depends on both the effective dielectric constant and the effective magnetic permeability.
The propagation constant of the TEM mode is given by
\[ \beta=\omega\sqrt{\mu_0\mu_{r\mathrm{eff}}\epsilon_0\epsilon_{\mathrm{eff}}} \]
where \(\beta\) is the phase constant, \(\omega\) is the angular frequency, \(\mu_0\) is the permeability of free space, \(\mu_{r\mathrm{eff}}\) is the effective relative permeability of the ferrite-loaded transmission line, \(\epsilon_0\) is the permittivity of free space, and \(\epsilon_{\mathrm{eff}}\) is the effective relative dielectric constant of the microstrip structure.
The equation demonstrates directly why changing the ferrite magnetization changes the phase response. If the magnetization direction changes, the effective permeability \(\mu_{r\mathrm{eff}}\) changes. Since \(\mu_{r\mathrm{eff}}\) appears inside the square root, the propagation constant \(\beta\) also changes. For a fixed microstrip length \(l\), the phase accumulated by the signal is
\[ \phi=\beta l \]
Therefore, two different magnetization states that produce two different phase constants, \(\beta_1\) and \(\beta_2\), produce two different accumulated phases for exactly the same physical length. The resulting phase difference is
\[ \Delta\phi=(\beta_1-\beta_2)l \]
This is the fundamental phase-shifting mechanism of the reciprocal MIC ferrite phase shifter. The physical transmission-line length remains unchanged, while the electrical length is changed through the magnetic state of the ferrite. The device therefore provides electrical phase control without requiring a mechanically variable transmission path.
E. Wheeler Filling-Factor Concept
The fields of a microstrip transmission line are not completely confined inside the substrate. A portion of the electromagnetic field exists within the dielectric substrate while another portion extends into the surrounding region. Therefore, the effective dielectric constant experienced by the propagating wave is different from the actual relative permittivity \(\epsilon_r\) of the substrate material. A similar concept can be used to describe the effective magnetic response of a ferrite-loaded microstrip structure.
The effective dielectric constant can be represented using a dielectric filling factor \(q_e\), following the Wheeler filling-factor concept. It is expressed as
\[ \epsilon_{\mathrm{eff}}=1+q_e(\epsilon_r-1) \]
Here, \(\epsilon_r\) is the relative permittivity of the dielectric substrate and \(q_e\) represents the fraction of the electromagnetic field that effectively interacts with the dielectric material. For the approximation used in the supplied material, the dielectric filling factor is taken as
\[ q_e\approx0.6 \]
This means that the effective dielectric constant is determined not only by the substrate permittivity but also by the field distribution around the microstrip line. The filling factor accounts approximately for the fact that the microwave field experiences both the substrate and the surrounding medium.
A similar filling-factor approach can be applied to the magnetic response of the ferrite substrate. Instead of assuming that the entire magnetic field interacts with the ferrite in exactly the same manner, a magnetic filling factor \(q_m\) is introduced. The effective magnetic permeability can then be related to the permeability of the ferrite through the magnetic filling factor.
The magnetic filling factor can be expressed as
\[ q_m=\frac{\mu_{\mathrm{eff}}-1}{\mu_r-1} \]
Rearranging this relationship gives the corresponding effective magnetic permeability as
\[ \mu_{\mathrm{eff}}=1+q_m(\mu_r-1) \]
Here, \(\mu_r\) represents the relative permeability of the ferrite material, while \(\mu_{\mathrm{eff}}\) represents the effective permeability experienced by the microwave mode. The filling factor \(q_m\) therefore accounts for the actual distribution of the RF magnetic field and the fraction of that field that interacts with the ferrite material.
The introduction of \(q_m\) is important because a microstrip transmission line does not produce a uniform magnetic field entirely contained inside the ferrite substrate. The actual RF field occupies a distributed region around the conductor. Consequently, the effective magnetic response of the complete microstrip structure is generally different from the intrinsic permeability of the ferrite material itself.
F. Phase Constant for Different Magnetization Directions
The two principal magnetization directions produce different effective permeabilities and therefore different phase constants. When the ferrite is magnetized parallel to the microstrip line, the RF interaction is maximum and the propagation constant is significantly affected by the ferrite magnetic response. When the ferrite is magnetized perpendicular to the microstrip line, the interaction is very small and the effective permeability is approximately unity.
For the perpendicular magnetization state, the effective permeability can be approximated by
\[ \mu_{r\mathrm{eff},\perp}\approx1 \]
Substitution into the TEM propagation equation gives an approximate phase constant of
\[ \beta_{\perp}\approx \omega\sqrt{\mu_0\epsilon_0\epsilon_{\mathrm{eff}}} \]
This represents the phase constant when the ferrite produces very little additional magnetic interaction with the RF field. The propagation behavior in this state is therefore primarily determined by the dielectric loading of the microstrip structure.
For parallel magnetization, the effective permeability differs from unity because of the strong ferrite interaction. Using the effective permeability associated with the parallel state, the phase constant can be written in the general form
\[ \beta_{\parallel}= \omega\sqrt{\mu_0\mu_{r\mathrm{eff},\parallel}\epsilon_0\epsilon_{\mathrm{eff}}} \]
The exact value of \(\beta_{\parallel}\) depends on the ferrite magnetic parameters, operating frequency, saturation magnetization, and magnetic filling factor. Since \(\mu_{r\mathrm{eff},\parallel}\) differs from the approximately unity value associated with perpendicular magnetization, the two propagation constants are different.
The supplied analysis considers the particular case in which the magnetic filling factor is
\[ q_m=0.5 \]
With this value, the effective magnetic response of the microstrip structure represents approximately half of the corresponding intrinsic magnetic contribution according to the filling-factor model. The resulting expressions for the parallel and perpendicular phase constants show explicitly that the parallel state contains the frequency-dependent ferrite magnetic terms, whereas the perpendicular state remains approximately equivalent to the non-magnetic reference condition.
Using the small-field approximation for the ferrite response, the parallel phase constant can be expressed in the form
\[ \beta_{\parallel} \approx \omega\sqrt{\mu_0\epsilon_0\epsilon_{\mathrm{eff}}} \sqrt{ \left[2-\left(\frac{\omega_m}{\omega}\right)^2\right] \left[2-2\left(\frac{\omega_m}{\omega}\right)^2\right] } \]
while for perpendicular magnetization, where the ferrite interaction is approximately negligible, the phase constant becomes
\[ \beta_{\perp} \approx \omega\sqrt{\mu_0\epsilon_0\epsilon_{\mathrm{eff}}} \]
The important result is not merely the individual expressions but the fact that \(\beta_{\parallel}\neq\beta_{\perp}\). The direction of ferrite magnetization therefore provides electrical control over the phase constant. When the ferrite is switched between the two magnetization states, the microwave signal experiences different phase accumulation even though the physical microstrip length remains unchanged.
G. Fractional Change in Phase Constant
The phase-shifting capability can be quantified by considering the difference between the phase constants corresponding to the two magnetization states. Let \(\beta_{\parallel}\) represent the phase constant when the ferrite is magnetized parallel to the microstrip line and let \(\beta_{\perp}\) represent the phase constant when the ferrite is magnetized perpendicular to the line. The difference between these two values represents the change in propagation characteristics produced by changing the magnetization direction.
The fractional change in phase constant can be expressed as
\[ \frac{\Delta\beta}{\beta} = \frac{\beta_{\parallel}-\beta_{\perp}} {\beta_{\perp}} \]
Using the phase-constant expressions obtained from the ferrite effective-permeability model, the fractional change can be written in terms of the frequency ratio \(\omega_m/\omega\). For the \(q_m=0.5\) case, the supplied analysis gives the corresponding relationship in terms of the parallel and perpendicular propagation constants. This relationship shows that the fractional phase-constant change is governed by the magnetic response of the ferrite and therefore depends on the operating frequency relative to the characteristic frequency \(\omega_m\).
The phase shift produced by the change in magnetization follows directly from the change in propagation constant. If the physical length of the ferrite-loaded microstrip is \(l\), the phase accumulated in the two magnetic states is
\[ \phi_{\parallel}=\beta_{\parallel}l \]
and
\[ \phi_{\perp}=\beta_{\perp}l \]
Therefore, the differential phase shift obtained by switching the magnetization direction is
\[ \Delta\phi = \phi_{\parallel}-\phi_{\perp} = (\beta_{\parallel}-\beta_{\perp})l \]
This equation connects the magnetic behavior of the ferrite directly to the practical phase-shifting function of the microwave device. The difference in phase constants is generated by the different effective permeabilities associated with the two magnetization directions, while the physical length \(l\) determines how much of this propagation-constant difference is accumulated.
Thus, a longer ferrite-loaded microstrip section produces a larger phase difference for the same difference in propagation constants. Similarly, increasing the difference between \(\beta_{\parallel}\) and \(\beta_{\perp}\) increases the phase shift obtained for a fixed physical length. The phase-shifter design therefore involves both the electromagnetic properties of the ferrite and the physical dimensions of the microstrip structure.
The complete operating principle of the reciprocal ferrite phase shifter can therefore be summarized through the chain of electromagnetic relationships: changing the direction of magnetization changes the interaction between the ferrite and RF magnetic field, this changes the effective permeability, the effective permeability changes the propagation constant, and the propagation constant determines the phase accumulated along the fixed microstrip length. The resulting difference in accumulated phase is the required electrically controlled phase shift.
Reciprocal Phase-Shifter Configuration
A reciprocal ferrite phase shifter can be constructed using a microstrip transmission line formed on a ferrite substrate, together with suitable DC magnetizing arrangements for controlling the state of the ferrite. The practical configuration is designed so that the microwave signal travels through a compact ferrite-loaded transmission path while the magnetization of the ferrite can be changed electrically. The change in magnetization modifies the effective RF permeability and consequently changes the propagation constant of the microwave signal. Since the physical length of the transmission line remains fixed, changing the propagation constant changes the electrical length of the line and produces the required phase shift.
Both analog-controlled and digital-controlled reciprocal phase shifters can be implemented using this configuration. In the analog version, the magnetizing current can be varied to change the magnitude or direction of the magnetization and therefore obtain a continuously controllable phase response. In the digital version, selected magnetization states are established using current pulses, allowing the phase shifter to operate between predetermined phase states. A compact meander configuration is particularly useful because it provides a long effective microwave path within a relatively small physical package.
3. Reciprocal Phase-Shifter Configuration
The configuration of a reciprocal ferrite phase shifter is based on four closely related elements: a ferrite-loaded microstrip transmission line, suitable spacing between adjacent portions of the line, DC magnetizing wires, and a control arrangement for selecting the required magnetization state. The microstrip carries the RF signal, while the DC wires establish the static magnetic field required to magnetize the ferrite. The physical arrangement of these elements is important because the RF magnetic field must interact with the ferrite strongly enough to produce a useful phase shift while unwanted coupling between adjacent transmission-line sections must be kept sufficiently small to preserve reciprocal operation.
A. Meander Microstrip Configuration
A meander microstrip configuration is used to obtain a long effective transmission-line path within a compact physical area. Instead of extending the microstrip conductor as a single straight line, the conductor is folded into a series of adjacent sections. The microwave signal therefore travels through a substantially longer electrical path than would be possible with a straight line occupying the same package dimensions.
The use of a meander structure is particularly useful for ferrite phase shifters because the phase shift is proportional to the propagation distance. For a transmission-line length \(l\), the accumulated phase is related to the phase constant by
\[ \phi=\beta l \]
Consequently, a longer effective microstrip path allows a larger phase shift to be obtained from the same change in propagation constant. Rather than increasing the external dimensions of the device to accommodate a long straight transmission line, the conductor is folded into a compact meander pattern. This reduces the overall physical size of the phase shifter while retaining the required microwave interaction length.
The meander configuration can be used for both analog reciprocal phase shifters and digital reciprocal phase shifters. In an analog phase shifter, the magnetic state of the ferrite is varied continuously or over a continuous range, and the meander line provides the required interaction length for the resulting phase variation. In a digital phase shifter, the same type of compact transmission structure can be combined with discrete magnetic states so that switching the magnetization produces predetermined phase states.
The compact structure is therefore not merely a method of reducing the size of the physical circuit. It also allows the designer to obtain a useful phase shift within a practical microwave package. The meander line provides the necessary propagation length while the ferrite substrate provides electrical control over the propagation constant.
B. Loose Coupling Between Adjacent Lines
Although the meander structure places several sections of the microstrip conductor close to one another, the adjacent sections in a reciprocal phase shifter are intentionally kept sufficiently far apart to minimize unwanted RF coupling. If adjacent microstrip sections are strongly coupled, electromagnetic energy from one section can interact significantly with neighboring sections. Such interaction can modify the intended RF magnetic-field distribution and may introduce unwanted non-reciprocal behavior.
For the reciprocal configuration, the spacing \(d\) between adjacent meander lines is selected to be greater than five times the substrate height \(h\). The condition is
\[ d>5h \]
Here, \(d\) represents the spacing between adjacent portions of the meander microstrip conductor and \(h\) represents the height of the ferrite substrate. Maintaining this spacing makes the electromagnetic coupling between neighboring line sections sufficiently small for practical purposes. The individual sections can therefore behave more like separate portions of the intended transmission path rather than strongly interacting coupled lines.
The requirement \(d>5h\) is especially important because the microstrip electromagnetic field extends beyond the conductor and into the surrounding substrate and space. If adjacent conductors are placed too close together, the fields associated with one section can overlap substantially with those of the neighboring section. This coupling can alter the effective propagation characteristics and can interfere with the desired reciprocal phase-shifting mechanism.
By keeping the adjacent lines loosely coupled, the reciprocal configuration minimizes unwanted RF interaction between neighboring meander sections. This helps maintain the intended relationship between ferrite magnetization, effective permeability, propagation constant, and phase shift. The spacing is therefore an important part of the electromagnetic design rather than simply a mechanical packaging consideration.
The distinction between loose coupling in the reciprocal phase shifter and close coupling in the non-reciprocal phase shifter is particularly important. In the reciprocal configuration, the adjacent lines are separated sufficiently to suppress significant RF coupling and avoid unwanted non-reciprocal effects. In contrast, the non-reciprocal configuration intentionally uses closely spaced microstrip sections so that their RF magnetic fields interact. When the appropriate quarter-wavelength spacing and phase relationship are introduced, this strong interaction produces a circularly polarized RF magnetic field. That mechanism is used to obtain differential interaction with the magnetized ferrite and hence non-reciprocal phase shifting.
C. DC Magnetizing Wires
I. Magnetizing Wires Through the Substrate
The magnetization of the ferrite substrate is controlled using DC-current-carrying wires positioned through suitable holes in the substrate. In the reciprocal phase-shifter configuration, the magnetizing wires pass through the locations identified as \(1\)-\(1'\) and \(2\)-\(2'\). When DC current flows through these wires, the current produces a static magnetic field in the surrounding ferrite material.
The magnetic field generated by a current-carrying conductor depends on the magnitude and direction of the current. Therefore, by controlling the current through the magnetizing wires, the direction and state of magnetization of the ferrite substrate can be controlled. The microwave signal itself does not need to be interrupted or mechanically redirected to change its phase. Instead, the magnetic environment through which the RF signal propagates is changed electrically.
The positions of the wires are selected so that their generated magnetic fields establish the required magnetization directions within the ferrite. In the configuration described here, the two magnetizing-wire arrangements correspond to the two principal magnetic states used for reciprocal phase shifting. The wires therefore provide the interface between the electrical control circuit and the magnetic state of the ferrite substrate.
II. Magnitude and Direction of Magnetization
The applied DC current determines the strength of the magnetic field produced by the magnetizing wire and consequently affects the magnetization of the ferrite. In an analog-controlled phase shifter, changing the magnitude of the applied current can change the magnetic state continuously, producing a corresponding change in effective permeability and propagation constant. The phase shift can therefore be controlled over a range of values rather than being restricted to only two discrete states.
The direction of the magnetization can also be controlled by changing the direction of the applied magnetic field. Reversing or redirecting the magnetizing current changes the orientation of the magnetic field produced by the conductor, allowing the ferrite magnetization to be established in a different direction. Because different magnetization directions produce different effective RF permeabilities, changing the magnetization direction changes the phase constant of the microstrip transmission line.
The resulting relationship can be viewed as a sequence of electromagnetic conversions. The control current establishes the static magnetic field, the static magnetic field establishes the ferrite magnetization, the magnetization determines the effective RF permeability, and the effective permeability determines the propagation constant. The resulting change in propagation constant produces a change in the phase accumulated by the microwave signal along the fixed microstrip length.
D. Digital Reciprocal Phase Shifter
A digital reciprocal phase shifter uses the same basic ferrite and microstrip structure but operates between predetermined magnetic states rather than continuously varying the magnetization. The digital behavior is obtained by using suitable magnetizing current pulses to establish selected states of the ferrite. Once the required magnetic state has been established, the ferrite can retain that state when a high-remanence material is used, allowing the phase shifter to operate as a latching device.
I. Two Magnetization States
In the configuration described here, two distinct magnetization states are established in the ferrite substrate. These states correspond to different orientations of the ferrite magnetization relative to the microstrip line. Because the RF interaction is different for the two orientations, each magnetic state produces a different effective permeability and therefore a different propagation constant.
If the two phase constants are represented by \(\beta_1\) and \(\beta_2\), the corresponding phase shifts through a microstrip section of length \(l\) are
\[ \phi_1=\beta_1l \]
and
\[ \phi_2=\beta_2l \]
The difference between the two digital phase states is therefore
\[ \Delta\phi=(\beta_1-\beta_2)l \]
Thus, the digital operation does not mean that the microwave signal itself is digitally encoded. Instead, the magnetic state of the ferrite is switched between discrete states, and each magnetic state corresponds to a predetermined microwave phase response. This makes it possible to use the phase shifter as a digitally controlled microwave component.
II. Selection of Magnetization State
The two magnetization states can be selected by applying DC current through the appropriate magnetizing-wire arrangement. Current through the \(1\)-\(1'\) wire arrangement establishes the magnetization state associated with perpendicular magnetization, while current through the \(2\)-\(2'\) arrangement establishes the state associated with parallel magnetization. The two arrangements therefore provide electrical selection between the two phase-shift states.
For the configuration described in the source material, the \(1\)-\(1'\) path is associated with perpendicular magnetization. In this state, the interaction between the ferrite and the RF magnetic field is very small, giving an effective RF relative permeability approximately equal to unity. The corresponding propagation constant is therefore close to that of the reference microstrip structure without significant magnetic loading.
The \(2\)-\(2'\) path is associated with parallel magnetization. In this state, the ferrite has maximum interaction with the RF magnetic field, and the effective permeability is determined by the magnetized-ferrite response. The propagation constant consequently differs from that of the perpendicular state.
Switching between the \(1\)-\(1'\) and \(2\)-\(2'\) magnetizing arrangements therefore switches the ferrite between two magnetic conditions and produces two corresponding phase states. In a latching implementation, current pulses can be used to establish the required state without requiring continuous DC current to maintain the magnetic condition. This is particularly useful for low-power digital microwave control systems.
E. Overall Reciprocal Phase-Shifter Operation
The complete operation of the reciprocal phase shifter begins with microwave propagation along the ferrite-loaded meander microstrip line. The RF signal produces an electromagnetic field around the microstrip conductor, including an RF magnetic field that interacts with the magnetized ferrite substrate. The strength and nature of this interaction depend on the orientation of the static ferrite magnetization relative to the microstrip line.
The magnetizing wires provide electrical control over this magnetic state. When the appropriate DC current is applied through the \(1\)-\(1'\) or \(2\)-\(2'\) arrangement, a static magnetic field is generated and the ferrite is magnetized in the required direction. The resulting magnetization state determines the effective RF relative permeability. In the perpendicular state, the effective RF relative permeability is approximately unity, while in the parallel state the stronger magnetic interaction produces a different effective permeability.
The change in effective permeability produces a change in the propagation constant according to
\[ \beta=\omega\sqrt{\mu_0\mu_{r\mathrm{eff}}\epsilon_0\epsilon_{\mathrm{eff}}} \]
Since the phase accumulated along the microstrip is given by
\[ \phi=\beta l \]
a change in \(\beta\) directly produces a change in the microwave phase. The phase-shifting action is therefore achieved without physically changing the length of the transmission line. The magnetic state changes the electrical length of the fixed physical line.
The meander structure makes this arrangement compact by providing a relatively long microwave path in a small physical area. At the same time, the spacing condition \(d>5h\) keeps neighboring sections sufficiently loosely coupled so that unwanted RF interaction is minimized and reciprocal operation is maintained. The magnetizing wires provide the means for electrically controlling the ferrite state, allowing the same basic configuration to support either analog or digital phase control.
In an analog reciprocal phase shifter, the applied magnetic field can be varied to change the magnetization condition and hence obtain a continuously variable phase response. In a digital reciprocal phase shifter, discrete magnetization states are selected using controlled current pulses, producing predetermined phase states. In both cases, the fundamental operating sequence remains the same: magnetic-field control changes ferrite magnetization, ferrite magnetization changes effective permeability, effective permeability changes propagation constant, and the change in propagation constant produces the required phase shift.
Non-Reciprocal Phase Shifter and Practical Parameters
A non-reciprocal ferrite phase shifter uses the interaction between a magnetized ferrite substrate and a carefully controlled RF magnetic field to produce different phase shifts for microwave propagation in opposite directions. Unlike the reciprocal configuration, where adjacent meander-line sections are intentionally separated to minimize RF coupling, the non-reciprocal configuration makes use of closely spaced microstrip sections. The close coupling between these sections produces a specially oriented RF magnetic field whose polarization changes along the transmission structure. When this RF field interacts with a ferrite magnetized along the direction of the microstrip lines, reversing the direction of magnetization changes the nature of the interaction and produces a differential phase response.
The non-reciprocal phase-shifter configuration therefore combines three important features: a compact meander microstrip structure, strong electromagnetic coupling between selected adjacent line sections, and controlled ferrite magnetization. The close coupling is not an unwanted effect in this case. Instead, it is deliberately introduced so that the RF magnetic fields associated with neighboring microstrip sections combine with the required amplitude, orientation, and phase relationship. At the centre of the coupled sections, this produces a circularly polarized RF magnetic field, which is the fundamental electromagnetic mechanism used to obtain non-reciprocal ferrite interaction.
4. Non-Reciprocal Phase Shifter
The operating principle of a non-reciprocal phase shifter is based on the directional response of a magnetized ferrite to an RF magnetic field. A ferrite is a gyrotropic magnetic material, meaning that its electromagnetic response depends on the relationship between the static magnetization and the RF field. When the direction of the magnetization is reversed, the interaction with a circularly polarized RF magnetic field can change in a direction-dependent manner. This produces different propagation conditions and therefore different phase shifts for opposite propagation directions or different magnetization states.
A. Meander Microstrip Configuration
The non-reciprocal phase shifter uses a meander microstrip configuration to obtain a relatively long microwave interaction path in a compact physical structure. The microstrip conductor is folded into adjacent sections rather than being implemented as one long straight transmission line. This reduces the overall physical size while providing sufficient transmission-line length for the ferrite interaction to accumulate into a useful phase shift.
In the reciprocal configuration discussed previously, adjacent meander sections are loosely coupled and are separated by a distance satisfying approximately
\[ d>5h \]
where \(d\) is the spacing between adjacent lines and \(h\) is the substrate height. This large spacing minimizes unwanted RF coupling and helps preserve reciprocal operation. The non-reciprocal configuration deliberately uses the opposite approach. Adjacent microstrip sections are placed closely together so that appreciable electromagnetic coupling occurs between them.
This close coupling causes the RF magnetic fields produced by neighboring conductors to interact strongly. The line arrangement and electrical length are selected so that the magnetic-field components at a particular point between the adjacent lines have the required spatial orientation and phase relationship. Therefore, coupling that is suppressed in the reciprocal phase shifter becomes an essential part of the operating mechanism in the non-reciprocal phase shifter.
B. Circularly Polarized RF Magnetic Field
I. Closely Coupled Microstrip Lines
In the non-reciprocal phase-shifter configuration, adjacent portions of the meander microstrip line are closely coupled. The reduced spacing allows the electromagnetic fields surrounding one conductor to interact significantly with those surrounding the neighboring conductor. In particular, the RF magnetic fields associated with the two microstrip sections combine in the region between them.
The purpose of this close coupling is not simply to increase the magnitude of the RF field. More importantly, it allows the fields generated by the neighboring conductors to form a controlled vector combination. The geometry of the microstrip sections and their electrical phase relationship determine the resulting polarization of the magnetic field at the selected observation point.
II. Quarter-Wavelength Sections
The adjacent microstrip sections are designed with an electrical length of approximately one-quarter wavelength at the centre frequency of operation. The condition can be represented as
\[ l\approx\frac{\lambda}{4} \]
where \(l\) is the relevant electrical length of the microstrip section and \(\lambda\) is the wavelength at the centre frequency. The quarter-wavelength condition is important because a propagation distance of \(\lambda/4\) corresponds to an electrical phase shift of \(90^\circ\).
The quarter-wavelength relationship follows from the phase constant and wavelength relation
\[ \beta=\frac{2\pi}{\lambda} \]
and therefore the phase change over a quarter wavelength is
\[ \beta\frac{\lambda}{4} = \frac{2\pi}{\lambda}\frac{\lambda}{4} = \frac{\pi}{2} = 90^\circ \]
Thus, the quarter-wavelength geometry provides the required phase relationship between the RF currents at corresponding points of the adjacent microstrip sections. This phase difference is essential for producing the circularly polarized RF magnetic field.
III. Magnetic-Field Components at Point P
Consider a point P located between two closely coupled adjacent microstrip sections. Each microstrip conductor produces an RF magnetic field in the region surrounding the conductor. Because the two conductors have different spatial positions and their RF currents have a controlled phase relationship, the magnetic fields produced by them at point \(P\) have different spatial orientations.
The total RF magnetic field at point \(P\) is obtained from the vector combination of the magnetic-field components produced by the two neighboring microstrip sections. If the two components are represented generally by \(\mathbf{H}_1\) and \(\mathbf{H}_2\), the resulting RF magnetic field can be written conceptually as
\[ \mathbf{H}_{\mathrm{RF}}=\mathbf{H}_1+\mathbf{H}_2 \]
The important feature is that these two components are not simply parallel fields that add along the same direction. Their spatial orientations are approximately perpendicular at the centre point \(P\). Consequently, their relative phase becomes critical in determining the trajectory of the resultant RF magnetic-field vector.
IV. Spatial Orthogonality of Field Components
Because of the geometry of the closely coupled microstrip sections, the two magnetic-field components at point \(P\) are spatially orthogonal. Spatial orthogonality means that the two field components act along mutually perpendicular directions. If the components are represented by two perpendicular coordinate directions, they can be written conceptually as
\[ \mathbf{H}_{\mathrm{RF}} = H_x\hat{\mathbf{x}} + H_y\hat{\mathbf{y}} \]
where \(\hat{\mathbf{x}}\) and \(\hat{\mathbf{y}}\) represent perpendicular directions. The spatial orthogonality of the components is essential because two perpendicular field components can combine to produce circular or elliptical polarization when their relative phase is appropriate.
If the two components were parallel, a phase difference between them would not produce the same rotating magnetic-field vector required for circular polarization. The carefully selected microstrip geometry therefore performs an important electromagnetic function: it converts the fields of the adjacent conductors into two spatially orthogonal RF magnetic-field components at point \(P\).
V. 90° Current Phase Difference
The quarter-wavelength electrical length introduces a \(90^\circ\) phase delay between the RF currents at the corresponding positions of the adjacent microstrip sections. In particular, the RF current at the centre of line 2 is delayed by approximately \(90^\circ\) relative to the RF current at the centre of line 1 at the centre frequency.
The phase relationship can be expressed as
\[ \Delta\phi_I=90^\circ \]
This phase difference originates from the quarter-wavelength electrical length of the microstrip sections. Since the magnetic field generated by a microstrip conductor follows the time-varying RF current responsible for that field, the corresponding magnetic-field components also acquire the required phase relationship.
The combination of two spatially perpendicular magnetic-field components with a \(90^\circ\) phase difference is precisely the condition required for circular polarization when their magnitudes are equal or sufficiently close. Thus, the quarter-wavelength microstrip arrangement is responsible for establishing the temporal phase relationship, while the physical geometry of the adjacent conductors establishes the spatial orthogonality.
VI. Formation of Circular Polarization
At the centre point \(P\), the two RF magnetic-field components are approximately orthogonal in space and differ in phase by \(90^\circ\). When these components have appropriate magnitudes, their vector sum does not remain fixed in one direction. Instead, the resultant RF magnetic-field vector rotates with time.
For two equal-magnitude orthogonal components, the circularly polarized field can be represented in a general form as
\[ \mathbf{H}_{\mathrm{RF}}(t) = H_0\cos(\omega t)\hat{\mathbf{x}} + H_0\sin(\omega t)\hat{\mathbf{y}} \]
The two components have equal amplitude, are perpendicular in space, and differ in phase by \(90^\circ\). As time progresses, the resultant vector continuously changes direction while maintaining approximately constant magnitude. The magnetic-field vector therefore traces a circular path in the plane perpendicular to the relevant propagation or magnetization direction.
This produces a circularly polarized RF magnetic field at the centre region of the coupled microstrip structure. The circular polarization is particularly important for the ferrite phase shifter because a magnetized ferrite responds differently depending on the rotational sense of the RF magnetic field relative to its static magnetization. This directional magnetic interaction is the basis of the non-reciprocal phase-shifting effect.
VII. Polarization Away from the Centre
The RF magnetic field is not circularly polarized throughout the entire length of the coupled microstrip structure. At the centre point \(P\), the geometry and phase relationship are arranged to produce the strongest circular polarization condition. As the observation point moves away from the centre, the amplitudes and relative phase of the two magnetic-field components change, so the resultant polarization gradually changes.
Moving away from the centre, the polarization changes from circular polarization to elliptical polarization. In an elliptical polarization state, the resultant magnetic-field vector still rotates with time, but its magnitude or component balance causes the vector tip to trace an ellipse rather than a circle. Near the ends of the coupled sections, the field approaches a linear polarization condition, where the resultant RF magnetic-field vector oscillates primarily along one direction.
The spatial variation can therefore be understood as a continuous change in polarization along the coupled structure: the field is approximately circular near the centre, becomes elliptical away from the centre, and approaches linear polarization toward the ends. This controlled polarization distribution allows the ferrite to experience a spatially varying RF magnetic field while retaining a region in which the circularly polarized interaction responsible for non-reciprocal behavior is strongest.
C. Non-Reciprocal Ferrite Interaction
I. Magnetization Along the Microstrip Lines
For the non-reciprocal configuration, the ferrite substrate is magnetized along the direction of the microstrip lines. This orientation is different from the perpendicular magnetization state used as a low-interaction state in the reciprocal phase-shifter configuration. The longitudinal magnetization provides the appropriate relationship between the static magnetic field and the circularly polarized RF magnetic field produced by the closely coupled microstrip sections.
The static magnetization can be represented by a vector \(\mathbf{M}\), while the RF magnetic field at the centre region can be represented by \(\mathbf{H}_{\mathrm{RF}}\). Because the ferrite is magnetically biased, the response of the ferrite to the RF field depends not only on the magnitude of the RF field but also on its orientation and rotational sense relative to the static magnetization.
This directional dependence is the essential difference between an ordinary isotropic transmission medium and a magnetized ferrite. The ferrite does not respond identically to every possible orientation and rotational sense of the RF magnetic field. Consequently, the direction of magnetization becomes an important parameter in determining the phase response of the microwave transmission line.
II. Reversal of Magnetization
When the direction of ferrite magnetization is reversed, the relationship between the static magnetization and the rotating RF magnetic field also changes. The ferrite therefore experiences a different electromagnetic interaction. This change does not simply correspond to reversing the sign of an ordinary scalar permeability; rather, it changes the gyrotropic magnetic response associated with the magnetized ferrite.
For example, if the magnetization is initially directed along the microstrip structure, reversing the magnetization produces an oppositely directed magnetic bias. The circularly polarized RF magnetic field then interacts with the ferrite under the opposite magnetic bias condition. Because the magnetic response is directional, the resulting effective propagation characteristics are different from those associated with the original magnetization state.
Therefore, reversing the magnetization provides a practical method for changing the phase response of the non-reciprocal phase shifter. The magnetization state can be controlled electrically using the DC magnetizing arrangement, allowing the phase response to be switched without mechanically changing the microwave transmission path.
III. Differential Interaction with the RF Field
The circularly polarized RF magnetic field is particularly effective for producing a differential interaction with a magnetized ferrite. A circularly polarized field has a definite sense of rotation. Reversing the ferrite magnetization changes the relative orientation between the magnetic bias and this rotational RF field, causing the ferrite to exhibit a different effective magnetic response.
The effective permeability experienced by the microwave signal is consequently dependent on the magnetic state. Since the propagation constant depends on effective permeability, the propagation constant also changes when the magnetization direction is changed. In general, the propagation constant can be represented as
\[ \beta=\omega\sqrt{\mu_0\mu_{r\mathrm{eff}}\epsilon_0\epsilon_{\mathrm{eff}}} \]
When the effective permeability changes from one magnetic state to another, the corresponding propagation constant changes from \(\beta_1\) to \(\beta_2\). The difference is therefore
\[ \Delta\beta=\beta_1-\beta_2 \]
This differential propagation behavior is the electromagnetic basis of the non-reciprocal phase shifter. The important point is that the change originates from the direction-dependent ferrite interaction with the RF magnetic field rather than simply from a change in the physical length of the transmission line.
IV. Non-Reciprocal Differential Phase Shift
If the microwave signal propagates through a physical length \(l\) of the ferrite-loaded microstrip, the phase accumulated in a particular magnetic state is
\[ \phi=\beta l \]
For two different magnetic conditions, the corresponding phase difference becomes
\[ \Delta\phi=(\beta_1-\beta_2)l \]
In a non-reciprocal ferrite phase shifter, the two propagation conditions can correspond to different directions of magnetic bias or different propagation directions relative to the ferrite bias. Because the ferrite interaction depends on the directional relationship between the magnetization and the circularly polarized RF magnetic field, the phase response is not identical under the corresponding reversed condition.
The resulting differential phase shift is therefore a direct consequence of the gyrotropic behavior of the magnetized ferrite. The closely coupled microstrip sections create the required circular RF magnetic field, the ferrite magnetization establishes a preferred magnetic direction, and the interaction between these two fields produces different effective propagation conditions. This is what distinguishes the non-reciprocal phase shifter from the reciprocal configuration.
D. Digital/Latching Non-Reciprocal Phase Shifter
The non-reciprocal phase-shifting structure can also be implemented as a digital or latching phase shifter. Instead of continuously controlling the magnetic field, selected magnetization states are established using controlled current pulses. A sufficiently thin ferrite substrate and small magnetizing wires can be used to realize the required magnetic switching arrangement in a compact microwave package.
I. Thin Ferrite Substrate
A thin ferrite substrate is useful for obtaining a compact implementation of the non-reciprocal phase shifter. The microstrip conductor is formed on or in association with the ferrite substrate, while small holes can be provided through the substrate for the magnetizing wires. The thin structure reduces the physical volume of the component and makes it practical to integrate the RF transmission structure and magnetic control arrangement within a small housing.
The substrate thickness also affects the electromagnetic field distribution and therefore influences the interaction between the microstrip line and ferrite material. Consequently, substrate thickness is both a mechanical and an electromagnetic design parameter. In the practical structure described in the supplied material, a substrate height of 50 mil is used.
II. DC-Current Wires \(I_1\) and \(I_2\)
The magnetization of the ferrite is controlled using small DC-current-carrying wires identified as \(I_1\) and \(I_2\). These wires pass through suitable holes in the ferrite substrate. When a current pulse is applied to one of the wires, the resulting magnetic field changes the magnetization state of the ferrite.
The magnitude of the current influences the strength of the magnetic field generated around the wire, while the direction of current determines the direction of the corresponding magnetic field. Consequently, appropriate control of \(I_1\) and \(I_2\) allows the magnitude and direction of the ferrite magnetization to be changed. The magnetizing wires therefore perform the same fundamental control function as the magnetizing arrangements in the reciprocal phase shifter, but they are used here in a structure designed to exploit the non-reciprocal ferrite interaction.
III. Current Pulses
In the digital implementation, the ferrite is switched between magnetic states using current pulses. A pulse with sufficient amplitude produces the magnetic field required to magnetize the ferrite into the desired state. Once the ferrite has been magnetized, a high-remanence ferrite can retain a substantial portion of its magnetization after the external magnetizing current is removed.
This behavior produces a latching phase-shifter operation. The control circuit does not necessarily need to supply continuous DC current to maintain the selected magnetic state. Instead, a current pulse changes the state, and the ferrite retains that state until another suitable magnetic pulse changes it again. This reduces the steady-state control power and makes the phase shifter suitable for digitally controlled microwave systems.
The digital operation can therefore be understood as a sequence in which a control pulse is applied to the appropriate magnetizing wire, the resulting magnetic field changes the ferrite magnetization, the ferrite retains the selected state because of its remanence, and the microwave transmission line exhibits the phase response associated with that magnetic state. Applying another suitable pulse can switch the ferrite to another state and consequently change the microwave phase.
E. Practical Parameters
The practical characteristics of a non-reciprocal digital ferrite phase shifter can be described in terms of its phase-shift capability, physical dimensions, substrate thickness, insertion loss, operating bandwidth, and centre frequency. These parameters provide an indication of the electrical performance as well as the physical compactness of the device.
The supplied phase-shifter example provides a 1-bit phase shift of approximately \(360^\circ\pm10^\circ\). A one-bit implementation represents a basic digitally controlled phase-shifting state, while the specified phase range indicates the approximate phase-shifting capability of the practical device. The tolerance indicates that the achieved phase shift can vary around the nominal \(360^\circ\) value because of practical electromagnetic and fabrication effects.
The substrate has a physical size of approximately
\[ 1''\times1'' \]
This compact substrate dimension demonstrates one of the major advantages of using a meander microstrip structure. A relatively long microwave interaction path can be accommodated within a small physical area by folding the conductor into a compact configuration.
The substrate height is specified as 50 mil. The unit mil represents one-thousandth of an inch, so
\[ 1\ \text{mil}=0.001\ \text{inch} \]
Using the supplied conversion
\[ 1\ \text{mil}=0.0254\ \text{mm} \]
the 50 mil substrate height is
\[ 50\times0.0254=1.27\ \text{mm} \]
Therefore, the substrate height is approximately
\[ h=1.27\ \text{mm} \]
The reported insertion loss is 2.4 dB over a 10% bandwidth. Insertion loss represents the reduction in transmitted microwave power caused by the phase-shifter structure. The reported value includes the practical losses associated with the ferrite material, conductor, dielectric structure, coupling arrangement, and other physical characteristics of the microwave component.
The specified 10% bandwidth indicates the frequency range around the centre operating frequency over which the stated performance is considered applicable. If the centre frequency is \(f_0\), a 10% fractional bandwidth can be represented approximately by
\[ \frac{\Delta f}{f_0}=0.10 \]
For the supplied device, the centre frequency is
\[ f_0=5.75\ \text{GHz} \]
The centre frequency is important because the quarter-wavelength relationship used to generate the circularly polarized RF magnetic field is designed around this operating frequency. At the centre frequency, the relevant microstrip sections have the required electrical length and the RF currents have the intended \(90^\circ\) phase relationship. Away from the centre frequency, the electrical length changes, so the exact field polarization and ferrite interaction also change.
The practical parameters can therefore be summarized as follows:
| Parameter | Value |
|---|---|
| Phase shift | 1 bit, approximately \(360^\circ\pm10^\circ\) |
| Substrate size | \(1''\times1''\) |
| Substrate height | 50 mil |
| Equivalent substrate height | 1.27 mm |
| Insertion loss | 2.4 dB over 10% bandwidth |
| Centre frequency | 5.75 GHz |
Overall, the non-reciprocal ferrite phase shifter operates by intentionally coupling adjacent sections of a meander microstrip line and using their quarter-wavelength electrical relationship to generate a circularly polarized RF magnetic field near the centre of the structure. The ferrite is magnetized along the microstrip direction, and reversal of the magnetization changes the gyrotropic interaction between the ferrite and the RF magnetic field. This produces different propagation conditions and consequently a differential phase shift.
The digital or latching version adds electrical control to this electromagnetic mechanism. Small DC-current wires \(I_1\) and \(I_2\) can be used to establish the required magnetic states through current pulses. When a high-remanence ferrite is used, the selected magnetic state can be retained after the magnetizing pulse is removed. The result is a compact, electrically controlled microwave phase shifter capable of providing a large phase shift while maintaining a practical physical size.
The essential distinction between the two ferrite phase-shifter configurations is therefore clear. The reciprocal phase shifter uses loosely coupled meander sections to suppress unwanted RF interaction and obtains phase control mainly from the difference in effective permeability between magnetization states. The non-reciprocal phase shifter intentionally uses closely coupled sections and a quarter-wavelength arrangement to create a circularly polarized RF magnetic field. The directional interaction between this field and the magnetized ferrite produces the non-reciprocal differential phase response.