Microwave Circulator
Microwave Circulator: Fundamentals and Working Principle
A microwave circulator is a passive multiport microwave device that allows electromagnetic waves to travel from one port to the next port in a predetermined direction while preventing significant transmission in the reverse direction. It is a type of multiport waveguide junction in which the power flow is controlled by the non-reciprocal behavior of the device. Unlike a reciprocal microwave network, where transmission characteristics are the same in both directions, a circulator provides directional power flow between its ports. This makes it particularly useful for separating transmitted and received microwave signals in systems where the same antenna or transmission path is shared by different circuits.
In a general microwave circulator having multiple ports, the wave entering the \(n\)th port is directed toward the next port, represented as the \((n+1)\)th port, according to the circulation direction of the device. Thus, the power does not propagate arbitrarily between all ports. Instead, it follows a specific cyclic path determined by the construction and non-reciprocal properties of the circulator. There is no fundamental restriction on the number of ports that a circulator can have, although practical microwave systems commonly use three-port and four-port circulators. Among these, the four-port circulator is particularly important in microwave engineering and is the main configuration considered in this article.
Basic Operating Principle of a Microwave Circulator
The basic operation of a four-port microwave circulator can be understood by considering the ports as successive points in a cyclic power-flow path. When a microwave signal is applied to port 1, the device directs the signal to port 2. When the input is applied to port 2, the signal is directed to port 3. Similarly, an input at port 3 emerges from port 4, while an input at port 4 is directed back to port 1. Therefore, the ideal circulation sequence of a four-port circulator is port 1, port 2, port 3, port 4, and back to port 1.
This cyclic behavior means that the circulator provides transmission between each port and its immediate next port in one direction, while transmission in the reverse direction is suppressed. For example, a signal applied at port 1 is transferred to port 2, but a signal applied at port 2 does not travel backward to port 1. Instead, it continues in the prescribed circulation direction toward port 3. The same behavior occurs around the remaining ports, producing a continuous unidirectional circulation of microwave energy.
For an ideal four-port circulator, the desired power-transfer relationships can therefore be stated as follows:
- An input at port 1 emerges at port 2.
- An input at port 2 emerges at port 3.
- An input at port 3 emerges at port 4.
- An input at port 4 emerges at port 1.
At the same time, the reverse transmission paths between adjacent ports are ideally suppressed. Consequently, the circulator behaves as a non-reciprocal device in which the direction of power flow is determined by the circulation characteristic of the junction. This property distinguishes a microwave circulator from ordinary reciprocal junctions and allows it to perform signal-routing functions without requiring separate switching elements.
Principle of Operation
The operation of a microwave circulator depends fundamentally on non-reciprocal electromagnetic behavior. In practical circulators, the required non-reciprocity is commonly obtained using ferrite materials subjected to a suitable static magnetic field. The ferrite material modifies the propagation characteristics of electromagnetic waves differently depending on their direction of propagation and polarization. As a result, the device can be designed so that waves travelling in the desired direction reinforce at the appropriate output port, while waves that would produce an undesired transmission path are cancelled or strongly suppressed.\
Phase relationships and interference are also important in the operation of many circulator configurations. When an input signal is divided into multiple paths inside the device, the individual waves acquire different phase changes as they propagate through couplers, waveguide sections, and non-reciprocal phase-shifting elements. At a particular output port, the waves can arrive with the required phase relationship and combine constructively, allowing power to be transferred efficiently to that port. At another port, the same waves can arrive with a phase difference of \(180^\circ\), causing destructive interference and suppressing power transfer to that port.
Thus, the directional behavior of a microwave circulator is not simply a consequence of power division. It results from the combined action of non-reciprocity, controlled phase shifts, and interference between multiple signal paths. These principles are especially important when a four-port circulator is constructed using directional couplers and non-reciprocal phase shifters. In such a configuration, the phase changes introduced along different paths determine which port receives the signal and which port is isolated. The detailed phase analysis of this construction is considered in the subsequent sections of the article.
The fundamental physical principle behind practical ferrite circulators is Faraday rotation. When a circularly polarized electromagnetic wave propagates through a ferrite material subjected to an axial magnetic field, the magnetic bias causes the polarization state of the wave to rotate. The direction and amount of this rotation depend on the interaction between the electromagnetic wave and the magnetically biased ferrite. This rotation is non-reciprocal, meaning that the electromagnetic behavior for propagation in one direction is not simply the reverse of the behavior obtained when the wave travels in the opposite direction.
In a ferrite circulator, this non-reciprocal rotation is utilized to favor transmission from one port to the next while suppressing transmission in the opposite direction. In simplified terms, when a circularly polarized wave passes through a ferrite element affected by an axial magnetic field, its polarization axis rotates in a direction determined by the applied magnetic bias. The resulting change in the electromagnetic field distribution enables the circulator to distinguish between the permitted and suppressed directions of propagation.
Therefore, the Faraday rotation principle provides the physical basis for the non-reciprocal operation of many microwave circulators, while controlled phase relationships and interference are used in specific circuit and waveguide constructions to establish the required port-to-port circulation. Together, these principles allow a microwave circulator to route microwave power cyclically from one port to the next while providing strong isolation in the reverse direction.
Construction of a Four-Port Circulator Using Two 3 dB Directional Couplers
A four-port microwave circulator can be constructed using two 3 dB side-hole directional couplers, two waveguide paths, and two non-reciprocal phase shifters. The arrangement provides a controlled combination of signal splitting, phase shifting, and interference so that microwave power entering one port is directed to the next port in the circulation sequence. The four external ports are connected to the two directional couplers through a primary waveguide and a secondary waveguide. The two internal signal paths are arranged so that waves travelling through them acquire specific phase changes before reaching the output ports.
The two directional couplers are responsible for dividing the incident microwave signal into two equal components. Since each coupler is a 3 dB coupler, the incident power is divided equally between its two output paths. For an ideal 3 dB coupler, the magnitude of the relevant scattering coefficient is
\[ |S|=\frac{1}{\sqrt{2}} \]Thus, when a wave is applied to an input port of the coupler, each of the two resulting waves has an amplitude equal to \(1/\sqrt{2}\) times the incident wave amplitude. The two waves then travel through different paths and experience the phase changes associated with the directional couplers, waveguide sections, and non-reciprocal phase shifters.
Each 3 dB directional coupler also introduces the specified \(90^\circ\) phase relationship between its two coupled signal paths. This phase relationship is essential because the waves arriving at a particular output port must have the correct relative phase to combine constructively, while the waves arriving at an unwanted port must have a relative phase of \(180^\circ\) so that they cancel. Therefore, the operation of the circulator depends not only on equal power division but also on accurate control of the phase accumulated along the two paths.
The complete four-port structure can therefore be viewed as an interference network. Coupler 1 initially divides the input signal into two equal components. These components travel through the primary waveguide and secondary waveguide, respectively. The two non-reciprocal phase shifters introduce the required directional phase changes in the signal paths. Finally, Coupler 2 combines the signals. Depending on the port being considered, the resulting waves either add constructively or cancel destructively. This controlled interference produces the required circulation behavior.
Role of the Non-Reciprocal Phase Shifters
The non-reciprocal phase shifter is the key element that distinguishes this circulator arrangement from a network made only from ordinary reciprocal couplers and waveguides. A conventional reciprocal phase shifter produces the same phase behavior when the wave propagates in either direction. In contrast, a non-reciprocal phase shifter is designed so that the phase change depends on the direction of propagation through the device.
For the circulator considered here, the non-reciprocal phase-shifting behavior is represented by a \(180^\circ\) phase change in one propagation direction and \(0^\circ\) additional phase change in the opposite direction. Therefore, when a wave travels through the phase shifter in the direction that produces the non-reciprocal phase shift, its phase is changed by
\[ \Delta\phi=180^\circ \]When the same phase-shifting section is traversed in the opposite direction, the additional phase change is taken as
\[ \Delta\phi=0^\circ \]This directional phase behavior is essential for circulation. The two signal paths are otherwise arranged so that their propagation characteristics can be compared through their relative phase. The non-reciprocal phase shifters make the relative phase different when the signal travels in the opposite direction. Consequently, a signal that combines constructively at one port in the forward direction does not produce the same constructive combination when the propagation direction is reversed.
It is important to distinguish the phase contribution of the 3 dB directional coupler from that of the non-reciprocal phase shifter. The \(90^\circ\) phase relationship is associated with the directional coupler, whereas the \(180^\circ\) or \(0^\circ\) additional phase change is associated with the non-reciprocal phase shifter. The total phase at any output port is obtained by accounting for all phase changes encountered by the wave along its particular path.
Thus, the directional couplers determine how the signal is divided and establish the required quadrature phase relationship between the paths, while the non-reciprocal phase shifters introduce a direction-dependent phase change. The combination of these effects makes it possible to obtain constructive interference at the desired output port and destructive interference at the undesired port.
Signal Applied at Port 1
To understand the detailed working of the four-port circulator, consider a microwave signal applied at port 1. The incident wave first reaches directional coupler 1, where it is divided into two equal-amplitude components. One component propagates through the primary waveguide, while the other propagates through the secondary waveguide. Because the coupler is a 3 dB coupler, both components have the same amplitude, while their relative phase is determined by the \(90^\circ\) phase relationship of the coupler.
For the phase analysis, let the relevant phase quantities associated with the two paths be represented by \(w_1\), \(w_2\), \(w_3\), and \(w_4\), according to the phase convention used for the circulator diagram. The specified phase values are
\[ w_1=180^\circ \] \[ w_2=90^\circ \] \[ w_3=0^\circ \] \[ w_4=90^\circ \]These quantities represent the phase contributions associated with the different sections of the two signal paths. The phase at an output port is obtained by adding the phase contributions accumulated by each wave as it travels from the input through the corresponding coupler, waveguide path, and phase-shifting section. The important point is that the two waves arriving at a particular port must be compared with each other, because their relative phase determines whether the waves add or cancel.
Phase Analysis at Port 2
Consider first the two signal components that eventually reach port 2. The wave travelling through the primary path accumulates the phase contributions associated with that path and arrives at port 2 with a phase change of \(180^\circ\). The second wave travels through the alternative path and experiences the phase contributions of the directional couplers and the corresponding waveguide section. After accounting for these phase changes, the second wave also arrives at port 2 with a phase change of \(180^\circ\).
| Signal path | Phase at port 2 |
|---|---|
| Path through primary waveguide | \(180^\circ\) |
| Path through secondary waveguide | \(180^\circ\) |
Since both waves arrive at port 2 with the same phase, their relative phase difference is
\[ \Delta\phi_2=180^\circ-180^\circ=0^\circ \]A phase difference of \(0^\circ\) means that the two equal-amplitude waves combine constructively. Therefore, the energy supplied at port 1 is transferred efficiently to port 2. The equal power division at the first coupler does not prevent power from reaching port 2 because the two components are recombined with the proper phase relationship at the output.
This constructive combination is one of the most important features of the circulator. The signal does not simply travel through one physical path from port 1 to port 2. Instead, the input signal is divided into two components, and the phase relationships of those components are controlled so that they reinforce one another at the desired output port.
Phase Analysis at Port 4
Now consider the same input signal from port 1 at port 4. The two signal components follow different paths toward port 4. The wave travelling through the primary path passes through the appropriate phase-shifting and coupling sections and arrives at port 4 with a total phase change of \(270^\circ\). The other wave reaches port 4 with a total phase change of \(90^\circ\).
| Signal path | Phase at port 4 |
|---|---|
| Path through primary waveguide and phase shifter | \(270^\circ\) |
| Path through secondary waveguide | \(90^\circ\) |
The relative phase difference between the two waves at port 4 is therefore
\[ \Delta\phi_4=270^\circ-90^\circ \] \[ \Delta\phi_4=180^\circ \]Thus, the two equal-amplitude waves reaching port 4 are \(180^\circ\) out of phase. When two equal-amplitude waves have a phase difference of \(180^\circ\), their instantaneous field contributions are opposite and they cancel each other. Hence, ideally, no power is transferred from port 1 to port 4.
This destructive interference is the mechanism that provides isolation of the unwanted port. The same input signal that produces constructive interference at port 2 produces destructive interference at port 4 because the phase accumulated along the two paths is different for the two output locations. Therefore, the circulator directs the input power toward port 2 while suppressing its transmission toward port 4.
Phase Summary for an Input at Port 1
The complete phase information for the input applied at port 1 can be summarized using the following values. The phase quantities \(w_1\), \(w_2\), \(w_3\), and \(w_4\) describe the phase contributions according to the selected diagram and reference convention, while the final rows show the total phases of the two waves at the relevant output ports.
| Quantity | Phase |
|---|---|
| \(w_1\) | \(180^\circ\) |
| \(w_2\) | \(90^\circ\) |
| \(w_3\) | \(0^\circ\) |
| \(w_4\) | \(90^\circ\) |
| Arrival at port 2, path 1 | \(180^\circ\) |
| Arrival at port 2, path 2 | \(180^\circ\) |
| Arrival at port 4, path 1 | \(270^\circ\) |
| Arrival at port 4, path 2 | \(90^\circ\) |
The significance of these values is more important than the individual phase labels themselves. At port 2, the two waves have equal phase and therefore reinforce one another. At port 4, the waves differ by \(180^\circ\) and therefore cancel. Port 3 is the decoupled port for this input condition. Consequently, an input applied at port 1 is transferred to port 2, while the unwanted port 4 is isolated by destructive interference.
The operation can therefore be summarized as follows: port 1 produces two equal-amplitude signal components, the two components acquire controlled phase changes along separate paths, the components combine constructively at port 2, and they cancel at port 4. This establishes the first directional transmission characteristic of the four-port circulator. The same phase-control principle is applied for the other input ports to obtain circulation around the complete four-port network.
Complete Circulation Through the Four Ports
The operation of the four-port microwave circulator can now be extended to all four input ports. The analysis performed for an input at port 1 shows the basic mechanism: the incident wave is divided into two equal-amplitude components, the components travel through different paths and acquire controlled phase shifts, and the resulting waves combine constructively at the desired output port while cancelling at an unwanted port. Because the phase shifters are non-reciprocal, the phase relationship changes when the direction of propagation changes. This allows the same structure to direct power successively from one port to the next, producing the required cyclic circulation.
Signal from Port 1
When a microwave signal is applied at port 1, it first enters Coupler 1 and is divided into two equal-amplitude components. The two components propagate through the primary and secondary paths and experience the phase changes introduced by the directional couplers, waveguide sections, and non-reciprocal phase shifters. At port 2, the two waves arrive with the required phase relationship and combine constructively. From the phase analysis of the previous section, the two waves reaching port 2 have equal phase, while the two waves reaching port 4 differ in phase by \(180^\circ\).
\[ \Delta\phi_2=180^\circ-180^\circ=0^\circ \]Therefore, the waves at port 2 reinforce each other and maximum power transfer occurs at that port. At port 4, the corresponding waves have phases \(270^\circ\) and \(90^\circ\), giving
\[ \Delta\phi_4=270^\circ-90^\circ=180^\circ \]Hence, the waves at port 4 cancel ideally. Port 3 is the decoupled port for this excitation. Thus, an input at port 1 is transferred to port 2, establishing the first stage of circulation.
\[ P_1\rightarrow P_2 \]In words, power applied at port 1 emerges from port 2, while the undesired port is isolated through destructive interference.
Signal from Port 2
Next, consider a microwave signal applied at port 2. In this case, the signal enters Coupler 2 and is again divided into two equal-amplitude components. One component travels through the primary waveguide path, while the other travels through the secondary waveguide path containing the non-reciprocal phase-shifting section. Since the direction of propagation through the phase shifter is now different from the corresponding path in the port 1 excitation case, the phase contribution of the non-reciprocal phase shifter must be considered according to its propagation direction.
The two components propagate toward the opposite coupler and accumulate the phase changes associated with their respective paths. The phase shifts are arranged so that, at port 3, the two equal-amplitude waves arrive with the same effective phase. Their electric-field contributions therefore add constructively, producing the desired power transfer to port 3. At the unwanted port, the corresponding waves acquire a relative phase difference of \(180^\circ\), so they cancel each other ideally.
The important point is that the non-reciprocal phase shifters do not provide the same phase behavior for the two propagation directions. This directional phase characteristic changes the interference condition when the input is moved from port 1 to port 2. The constructive interference that previously occurred at port 2 is redirected so that the waves now reinforce at port 3.
\[ P_2\rightarrow P_3 \]Therefore, power applied at port 2 is transferred to port 3, while the corresponding reverse or unwanted path is suppressed by destructive interference.
Signal from Port 3
When the microwave signal is applied at port 3, the signal enters the circulator through the corresponding input side of the network and is divided into two equal-amplitude components. These components propagate through the two available paths toward Coupler 2. As in the previous cases, each wave accumulates a phase determined by the directional couplers, propagation paths, and non-reciprocal phase shifters.
For this direction of propagation, the phase relationships are such that the two components arrive at port 4 with the required phase alignment. The waves therefore combine constructively at port 4, allowing the microwave energy supplied at port 3 to appear at the next port in the circulation sequence. At the unwanted port, the phase difference between the two components becomes \(180^\circ\), producing destructive interference and ideally preventing power transfer to that port.
This behavior demonstrates that the same two-coupler structure can redirect the input signal from port 3 to port 4. The direction-dependent phase behavior of the non-reciprocal phase shifters ensures that the interference pattern changes appropriately for this propagation direction.
\[ P_3\rightarrow P_4 \]Hence, power applied at port 3 emerges from port 4, while transmission toward the unwanted port is suppressed.
Signal from Port 4
Finally, consider a microwave signal applied at port 4. The signal is divided into two equal-amplitude components and travels through the circulator in the direction that completes the cycle back toward port 1. The two components follow the primary and secondary paths and experience the phase changes associated with the directional couplers and the non-reciprocal phase shifters.
The most important difference in this case is the direction of propagation through the non-reciprocal phase-shifting sections. Because the phase shifter produces different phase behavior for opposite propagation directions, the phase accumulated by the two components is not the same as it would be for the corresponding forward path. The resulting phase relationship causes the two waves to combine constructively at port 1.
At the unwanted port, the same two waves arrive with a relative phase difference of \(180^\circ\). They therefore interfere destructively and ideally cancel. Consequently, the microwave energy supplied at port 4 is directed toward port 1 rather than being transferred toward port 3.
\[ P_4\rightarrow P_1 \]Thus, power applied at port 4 emerges from port 1. This completes the cyclic operation of the four-port circulator.
Complete Circulation Sequence
Combining the four input cases gives the complete operating sequence of the ideal four-port microwave circulator. An input at port 1 is directed to port 2, an input at port 2 is directed to port 3, an input at port 3 is directed to port 4, and an input at port 4 is directed back to port 1. Therefore, the power circulates continuously around the four ports in one prescribed direction.
The complete circulation sequence can be written as port 1, port 2, port 3, port 4, and back to port 1. This cyclic power flow is the defining characteristic of a four-port circulator. The device does not simply provide ordinary transmission between neighboring ports; rather, it provides non-reciprocal transmission, allowing power to move from each port to the next port in the specified direction while suppressing transmission in the reverse direction.
\[ 1\rightarrow2\rightarrow3\rightarrow4\rightarrow1 \]The complete operation therefore depends on the coordinated action of the 3 dB directional couplers and the non-reciprocal phase shifters. The couplers provide equal power division and the required \(90^\circ\) phase relationships, while the non-reciprocal phase shifters introduce direction-dependent phase changes. Together, these phase relationships cause constructive interference at the desired output port and destructive interference at the unwanted port for each excitation condition. This produces the characteristic one-way cyclic power flow of the four-port microwave circulator.
Four-Port Circulator Using Two Magic Tees and a Non-Reciprocal Phase Shifter
A four-port microwave circulator can also be constructed using two Magic Tees and a non-reciprocal \(180^\circ\) phase shifter. This is a separate construction from the arrangement using two 3 dB directional couplers. In this configuration, the required circulation is obtained by using the in-phase and out-of-phase combining properties of the Magic Tees together with the direction-dependent phase shift of the non-reciprocal phase shifter. The two Magic Tees are connected through two parallel paths, with one of the paths containing the non-reciprocal phase shifter.
Let the first Magic Tee be denoted by \(T_1\) and the second Magic Tee by \(T_2\). The four external ports of the circulator are associated with the H-arm and E-arm of these two Magic Tees. Port 1 is the H-arm of \(T_1\), while port 3 is the E-arm of \(T_1\). Similarly, port 2 is the H-arm of \(T_2\), while port 4 is the E-arm of \(T_2\).
The two Magic Tees are connected by two parallel paths. For clarity, let the two collinear-arm points of \(T_1\) be represented by \(b\) and \(d\), and the corresponding collinear-arm points of \(T_2\) be represented by \(a\) and \(c\). Thus, the upper connecting path joins \(c\) and \(d\), while the lower connecting path joins \(a\) and \(b\). The non-reciprocal phase shifter is placed in the lower connecting path. The upper path \(c\) to \(d\) does not contain the phase shifter.
The non-reciprocal phase shifter is assumed to provide a \(180^\circ\) phase shift in one propagation direction and \(0^\circ\) additional phase shift in the opposite propagation direction. This difference is essential to the operation of the circulator because the same connecting path produces different phase behavior depending on which Magic Tee is excited.
Magic Tee Properties Used in the Circulator
The operation of this circulator is based directly on the two fundamental signal-splitting properties of a Magic Tee. These properties determine whether the waves arriving at the connecting paths are in phase or \(180^\circ\) out of phase and therefore determine which arm of the receiving Magic Tee produces constructive or destructive interference.
H-Arm Excitation
When a microwave signal is applied to the H-arm of a Magic Tee, the signal divides equally between the two collinear arms. The two resulting waves have equal amplitude and the same phase. Therefore, the waves leaving the two collinear arms can be represented as two equal-amplitude in-phase signals.
When these two waves reach another Magic Tee while maintaining their in-phase relationship, they combine constructively at the H-arm and cancel at the E-arm. This property is used when power must be transferred from an H-arm of one Magic Tee to the H-arm of the other Magic Tee.
E-Arm Excitation
When a microwave signal is applied to the E-arm of a Magic Tee, the signal also divides equally between the two collinear arms, but the resulting waves have a \(180^\circ\) phase difference. Therefore, the two collinear-arm waves have equal amplitude and opposite phase.
When these two opposite-phase waves reach another Magic Tee, they combine constructively at its E-arm and cancel at its H-arm. These two Magic Tee properties provide the basic mechanism required for transferring power from one external port to the next while suppressing the unwanted port.
Signal Applied at Port 1
Consider first a microwave signal applied at port 1. Since port 1 is the H-arm of \(T_1\), the input signal is divided into two equal-amplitude, in-phase waves at the two collinear arms of \(T_1\). According to the defined internal points, these waves travel through points \(b\) and \(d\) toward \(T_2\).
The wave travelling through the upper path from \(d\) toward \(c\) does not pass through the non-reciprocal phase shifter. The other wave travels through the lower path from \(b\) toward \(a\), passing through the non-reciprocal phase shifter. For this direction of propagation, the phase shifter introduces \(0^\circ\) additional phase shift. Therefore, the two waves retain their original in-phase relationship when they reach \(T_2\).
Because the two waves arriving at \(T_2\) have equal amplitude and are in phase, they combine constructively at the H-arm, port 2. At the E-arm, port 4, the same in-phase waves produce cancellation. Hence, the input power is directed toward port 2 and is suppressed at port 4.
\[ 1\rightarrow2 \]Therefore, an input at port 1 is transferred to port 2. The combination of equal in-phase waves at \(T_2\) produces constructive interference at the H-arm and destructive interference at the E-arm.
Signal Applied at Port 2
Now consider a microwave signal applied at port 2. Port 2 is the H-arm of \(T_2\), so the input signal divides into two equal-amplitude, in-phase waves at the two collinear arms of \(T_2\). One wave travels through the upper connecting path from \(c\) toward \(d\), while the other travels through the lower connecting path from \(a\) toward \(b\).
The important difference from the previous case occurs in the lower path. The wave now travels through the non-reciprocal phase shifter in the opposite direction. For this direction of propagation, the phase shifter introduces an additional phase shift of \(180^\circ\). Consequently, although the two waves were initially in phase at the collinear arms of \(T_2\), they arrive at \(T_1\) with a \(180^\circ\) phase difference.
\[ \Delta\phi=180^\circ \]The two equal-amplitude waves arriving at \(T_1\) are therefore out of phase. The Magic Tee combines these opposite-phase waves constructively at its E-arm, port 3. At its H-arm, port 1, the same waves cancel each other. Thus, the signal is transferred to port 3 while port 1 remains isolated for this excitation.
\[ 2\rightarrow3 \]Therefore, an input at port 2 is transferred to port 3. The \(180^\circ\) directional phase shift introduced by the non-reciprocal phase shifter changes the phase relationship required for the signal to emerge from the E-arm of \(T_1\).
Signal Applied at Port 3
Next, apply the microwave signal to port 3, which is the E-arm of \(T_1\). An E-arm excitation produces two equal-amplitude waves at the collinear arms of \(T_1\), but these waves are \(180^\circ\) out of phase. Therefore, the waves travelling from points \(b\) and \(d\) toward \(T_2\) maintain an opposite-phase relationship.
The two waves travel through the upper and lower connecting paths toward \(T_2\). For this propagation direction, the phase relationship between the two paths is such that the required relative \(180^\circ\) phase difference is maintained when the waves reach \(T_2\). The two equal-amplitude opposite-phase waves therefore combine constructively at the E-arm of \(T_2\), which is port 4.
At the H-arm of \(T_2\), which is port 2, the opposite-phase waves cancel. Consequently, the power supplied at port 3 is directed to port 4, while port 2 is isolated from this excitation.
\[ 3\rightarrow4 \]Thus, an input at port 3 is transferred to port 4. The E-arm property of the Magic Tee is responsible for producing the required opposite-phase waves, which then combine at the E-arm of the receiving Magic Tee.
Signal Applied at Port 4
Finally, consider a microwave signal applied at port 4. Port 4 is the E-arm of \(T_2\), so the input signal divides into two equal-amplitude waves at the collinear arms of \(T_2\). These waves are \(180^\circ\) out of phase and travel toward \(T_1\) through the two connecting paths.
As the waves propagate from \(T_2\) toward \(T_1\), one of them passes through the non-reciprocal phase shifter. The direction of propagation is now the appropriate direction for the phase contribution to modify the original opposite-phase relationship. The additional phase change supplied by the non-reciprocal phase shifter causes the two waves to arrive at \(T_1\) with the required in-phase relationship.
The two equal-amplitude waves therefore combine constructively at the H-arm, port 1. At the E-arm, port 3, they cancel because the E-arm responds to the corresponding phase relationship with destructive interference. Hence, the input signal at port 4 is directed toward port 1 rather than toward port 3.
\[ 4\rightarrow1 \]Therefore, an input at port 4 is transferred to port 1. This final case completes the circulation through all four ports and demonstrates the importance of the direction-dependent phase shift of the non-reciprocal phase shifter.
Complete Circulation Using Two Magic Tees
The four signal-flow cases demonstrate that the two Magic Tee construction produces the same circulation behavior as the two 3 dB directional coupler construction. An input at port 1 is directed to port 2, an input at port 2 is directed to port 3, an input at port 3 is directed to port 4, and an input at port 4 is directed back to port 1.
\[ 1\rightarrow2\rightarrow3\rightarrow4\rightarrow1 \]The circulation is obtained by combining the in-phase and opposite-phase signal-splitting properties of the Magic Tees with the direction-dependent phase shift of the non-reciprocal phase shifter. The Magic Tees determine whether the waves combine at their H-arm or E-arm, while the non-reciprocal phase shifter changes the relative phase when the propagation direction is reversed. This controlled phase behavior makes one port the desired output and suppresses the unwanted port for each input condition.
S-Matrix, Ferrite Principle and Radar Application of a Microwave Circulator
S-Matrix of an Ideal Four-Port Circulator
The scattering matrix of an ideal four-port microwave circulator can be obtained directly from its circulation behavior. The defining operation of the device is that microwave power applied at one port appears at the next port in the prescribed direction. Thus, an input at port 1 is transferred to port 2, an input at port 2 is transferred to port 3, an input at port 3 is transferred to port 4, and an input at port 4 is transferred back to port 1. The scattering matrix must therefore represent these four allowed transmission paths while making the remaining transmission paths zero.
Since all four ports are assumed to be perfectly matched, there are no reflected waves at the input ports. Therefore, the diagonal elements of the scattering matrix are zero:
\[ S_{11}=S_{22}=S_{33}=S_{44}=0 \]The desired transmission paths have unity transmission for an ideal lossless circulator. From port 1 to port 2, the corresponding scattering parameter is \(S_{21}\). From port 2 to port 3, it is \(S_{32}\). From port 3 to port 4, it is \(S_{43}\). Finally, from port 4 to port 1, it is \(S_{14}\). Therefore,
\[ S_{21}=S_{32}=S_{43}=S_{14}=1 \]All other scattering parameters are zero because the ideal circulator does not transfer power through the unwanted paths. The complete scattering matrix is consequently
\[ \boxed{ [S]= \begin{bmatrix} 0&0&0&1\\ 1&0&0&0\\ 0&1&0&0\\ 0&0&1&0 \end{bmatrix} } \]The zero diagonal elements represent perfect matching at all four ports. An incident wave at any port therefore produces no reflected wave at that same port. The unit-magnitude transmission coefficients represent ideal power transfer from each port to the next port in the circulation direction.
The matrix also represents an ideal lossless network. Since the entire incident power is transferred to the designated output port and no power is dissipated inside the ideal device, the scattering matrix satisfies the lossless condition
\[ [S][S]^\dagger=[I] \]where \([I]\) is the identity matrix. In a practical circulator, some power is lost because of conductor loss, dielectric loss, ferrite loss, and other imperfections, so the transmission magnitude is slightly less than unity.
Most importantly, the scattering matrix is not symmetric. For a reciprocal network, the scattering parameters satisfy \(S_{ij}=S_{ji}\). In the circulator, however, the transmission from port 1 to port 2 is allowed, whereas the reverse transmission from port 2 to port 1 is suppressed. Thus,
\[ S_{21}=1 \] \[ S_{12}=0 \]Therefore,
\[ S_{12}\neq S_{21} \]This lack of symmetry is the mathematical representation of the non-reciprocal behavior of the circulator. The device permits power to travel cyclically in one direction while preventing the same power-transfer relationship in the reverse direction. Hence, non-reciprocity is the defining property that allows a circulator to perform directional microwave signal routing.
Three-Port Circulator
In addition to the four-port configuration, a three-port microwave circulator is widely used in microwave systems. A common three-port circulator can be constructed using a \(120^\circ\) H-plane waveguide or stripline symmetrical Y-junction with a central ferrite post or ferrite disc. A steady DC magnetic field \(H_0\) is applied along the axis of the ferrite element. The magnetically biased ferrite produces the required non-reciprocal electromagnetic behavior, causing microwave energy to propagate from one port to the immediate next port in the selected direction.
The direction of circulation depends on the properties of the ferrite material, the direction of the applied magnetic field, and the electromagnetic field configuration within the junction. Proper matching can be obtained by incorporating suitable tuning elements into the practical structure. With appropriate matching and reference-plane selection, the three-port circulator provides directional transmission around its three ports.
For a matched three-port circulator, the general scattering matrix can be written as
The zero diagonal elements represent matched ports, while the nonzero elements represent the allowed cyclic transmission paths. With properly selected reference planes, the phase reference can be chosen such that
\[ S_{13}=S_{21}=S_{32}=1 \]Therefore, the ideal three-port circulator has the scattering matrix
\[ \boxed{ [S]= \begin{bmatrix} 0&0&1\\ 1&0&0\\ 0&1&0 \end{bmatrix} } \]This matrix shows that an input at port 1 is transferred to port 2, an input at port 2 is transferred to port 3, and an input at port 3 is transferred back to port 1. The reverse transmission paths are suppressed. Thus, the three-port circulator exhibits the same fundamental non-reciprocal principle as the four-port circulator, although the number of ports and the physical construction are different.
For Different directionThe ideal three-port circulator has the scattering matrix
From this matrix, \(S_{21}=1\) means that a signal entering port 1 appears at port 2. Similarly, \(S_{32}=1\) means that a signal entering port 2 appears at port 3, while \(S_{13}=1\) means that a signal entering port 3 appears at port 1. Therefore, the circulation sequence is port 1, port 2, port 3, and back to port 1.
If the three ports are arranged around the junction in the same order as their physical numbering, this matrix represents circulation in the clockwise direction. The opposite circulation direction would require the nonzero transmission terms to be \(S_{12}\), \(S_{23}\), and \(S_{31}\), giving the reverse, or anticlockwise, circulation.
Ferrite and Faraday Rotation Principle
The physical basis of many practical microwave circulators is the non-reciprocal behavior of magnetically biased ferrite materials. A ferrite element is placed in the microwave structure and subjected to an external steady magnetic field. This magnetic bias changes the electromagnetic properties of the ferrite and causes the microwave field to interact with the material differently depending on its polarization and direction of propagation.
In the Faraday rotation principle, a circularly polarized microwave wave propagating through a ferrite material under an axial magnetic field experiences a rotation of its polarization. The rotation is associated with the magnetically biased ferrite medium and occurs in a direction determined by the applied magnetic field. A useful description of this behavior is that when a circularly polarized wave passes through a ferrite element affected by an axial magnetic field, its polarization axis rotates in the direction determined by the strength and direction of the magnetic bias.
The important feature for a circulator is that this rotation is non-reciprocal. Reversing the direction of propagation does not simply produce the same phase transformation in reverse. The magnetically biased ferrite therefore provides a direction-dependent electromagnetic response. This property can be combined with the geometry of the microwave junction so that energy is preferentially transferred from one port to the next while transmission in the opposite direction is suppressed.
Thus, Faraday rotation provides the fundamental physical mechanism behind the non-reciprocal behavior of ferrite circulators. In practical devices, the ferrite material, magnetic bias, junction geometry, and tuning elements are selected so that the desired circulation and impedance matching are obtained over the required microwave frequency range.
Microwave Circulator in Radar Applications
One of the important applications of a microwave circulator is in radar systems, where the same antenna is commonly required for both transmission and reception. The circulator provides a way to route the high-power transmitted signal toward the antenna while directing the much weaker received echo signal toward the radar receiver. At the same time, it provides isolation between the transmitter and receiver paths.
In a typical radar arrangement, the radar transmitter is connected to one port of the circulator, the antenna is connected to the next port in the circulation direction, and the radar receiver is connected to the following port. When the transmitter generates a microwave pulse, the circulator directs that signal toward the antenna. The antenna then radiates the microwave energy into the required region.
When the transmitted microwave pulse encounters an object, a portion of the energy is reflected back toward the radar antenna. The received microwave signal enters the circulator through the antenna port. Because the circulator operates in its prescribed direction, the received signal is directed toward the radar receiver rather than back toward the transmitter. In this way, the transmitter and receiver can share the same antenna while remaining electrically isolated from one another.
The circulator is particularly valuable in this application because the transmitted signal can be much more powerful than the received echo signal. Direct coupling of the transmitter output into the sensitive receiver could interfere with receiver operation. The non-reciprocal transmission characteristic of the circulator suppresses this unwanted direct transfer and provides the required transmitter-to-receiver isolation.
In a suitable multiport radar arrangement, the remaining port can also be connected to a matched termination when required. The matched termination absorbs unwanted power and prevents undesirable reflections from entering the circulator. Therefore, the circulator performs the combined functions of signal routing, transmitter and receiver isolation, and protection of the sensitive receiver from unwanted transmitted power.
Other Applications of Microwave Circulators
Because of their non-reciprocal power-flow characteristics, microwave circulators are used in several microwave and RF systems. Their ability to route signals between different ports while providing isolation in the reverse direction makes them useful wherever multiple microwave circuits must share a common signal path without directly interfering with one another.
- Radar systems: A circulator separates the transmitter and receiver paths when a common antenna is used for both transmission and reception.
- Duplexing: A circulator can provide directional separation between transmit and receive signals in a shared microwave system.
- Transmitter and receiver isolation: The non-reciprocal transmission characteristic prevents unwanted transmitter power from directly reaching sensitive receiver circuits.
- Antenna protection: The directional routing of microwave energy can help protect sensitive circuits from unwanted high-power signals.
- Microwave communication systems: Circulators can be used for directional signal routing and isolation between microwave subsystems.
- Measurement systems: The controlled direction of microwave power is useful in microwave test and measurement arrangements.
- Ferrite microwave devices: Circulators are important practical applications of the non-reciprocal properties of magnetically biased ferrite materials.
Performance Characteristics of a Practical Microwave Circulator
An ideal circulator is perfectly matched, lossless, and completely non-reciprocal, but practical microwave circulators cannot achieve these ideal conditions exactly. Real devices contain conductor losses, dielectric losses, ferrite losses, manufacturing tolerances, and imperfect matching. Consequently, a practical circulator exhibits a finite insertion loss and finite isolation between ports.
Typical performance values for practical three-port or four-port circulators can be represented by the following characteristics:
\[ \text{Insertion Loss}<1\text{ dB} \] \[ \text{Isolation}\approx30\text{ to }40\text{ dB} \] \[ \text{VSWR}<1.5 \]Insertion loss represents the reduction in power as the signal travels through the desired transmission path. In an ideal lossless circulator, the insertion loss would be zero, but practical material and conductor losses make it finite. Isolation represents how effectively the circulator suppresses power transfer through an unwanted direction. A higher isolation value indicates better suppression of the undesired transmission path. The VSWR indicates the quality of impedance matching at the ports, with a value close to unity representing better matching.
Therefore, the practical performance of a microwave circulator is determined by how closely its operation approaches the ideal conditions of low insertion loss, high isolation, and good port matching. The combination of these characteristics makes the circulator an important non-reciprocal microwave component for radar, communication, measurement, and other high-frequency systems.