Applications of Magic Tees
E-H Plane Junction Used for Impedance Measurement
The E-H Plane junction, also known as a Magic Tee or Hybrid Tee, is an important passive microwave component that can be used for measuring an unknown impedance. This application makes use of the different characteristics of the E-arm and H-arm of the junction. The H-arm acts as a sum port and provides equal-amplitude in-phase excitation to the two collinear arms, while the E-arm acts as a difference port and detects the difference between the signals associated with the two collinear branches. By connecting a microwave source to the H-arm and a null detector to the E-arm, the two collinear arms can be arranged as the branches of a microwave bridge. The unknown impedance can then be determined by adjusting the bridge until the null detector indicates a balanced condition.
1. E-H Plane Junction Is Used to Measure the Impedance
The E-H Plane junction is used for impedance measurement by forming a microwave bridge in which the two collinear arms act as the comparison branches. A microwave source is connected to the H-arm, while a null detector is connected to the E-arm. The two collinear arms are used for the measurement branches, with one branch associated with the unknown impedance and the other branch associated with a known reference or balancing condition. When microwave power is supplied to the H-arm, it is divided equally between the two collinear arms with the same phase. The signals then travel through the two branches and are affected by the impedances connected to them. The resulting waves return toward the E-H Plane junction, where their amplitude and phase relationships determine the signal appearing at the E-arm.
The operation is based on the bridge-balancing principle. Initially, if the unknown impedance and the reference branch do not produce the required relationship, the returning signals from the two collinear arms will not cancel completely at the E-arm. A resultant signal will therefore appear at the E-arm and will be detected by the null detector. The known reference branch or balancing element is then adjusted so that the response of the reference branch becomes properly related to the response of the unknown branch. When the required amplitude and phase conditions are achieved, the signals cancel at the difference port and the null detector indicates zero or minimum output. The unknown impedance can then be determined from the known reference condition and the adjustments required to obtain the null.
The connection of the source to the H-arm and the detector to the E-arm is important because the two arms perform different functions. The H-arm is a sum port, so an input signal applied to it produces equal-amplitude signals at the two collinear arms with the same phase. This provides symmetrical excitation to the two branches of the bridge. On the other hand, the E-arm is a difference port. Signals arriving from the two collinear arms combine at this port according to their relative amplitude and phase. Therefore, any imbalance between the two branches produces a detectable signal at the E-arm, while the balanced condition results in cancellation.
The impedance-measurement method is particularly suitable for microwave systems because impedance at microwave frequencies is represented by both magnitude and phase. An unknown impedance does not merely change the amplitude of a reflected wave; it can also change its phase. The E-H Plane junction provides a way of comparing these amplitude and phase changes through the bridge arrangement. Instead of directly measuring voltage and current as is commonly done at lower frequencies, the microwave system compares the wave responses of the unknown and reference branches. The null condition provides a well-defined point from which the unknown impedance can be evaluated.
1.a. Connection of the Microwave Source to the H-Arm
The microwave source is connected to the H-arm because the H-arm provides the required equal-amplitude in-phase excitation to the two collinear arms. When the source signal enters the H-arm, the incident microwave power is divided between the two collinear ports. For an ideal E-H Plane junction, the signals emerging from these two ports have equal magnitude and identical phase. This property is commonly described as the sum-mode behavior of the H-arm. It allows the two branches of the impedance-measurement bridge to receive a controlled and symmetrical microwave excitation.
The equal excitation of the two branches is important because the measurement depends on comparing their responses. If the unknown impedance is different from the reference impedance, the signals reflected from the two branches will generally have different amplitudes and phases. These differences are not caused by the initial excitation because the H-arm has supplied the two branches with equal-amplitude in-phase signals. Instead, they arise from the impedance conditions present in the two branches. The H-arm therefore establishes the common excitation required to make the subsequent comparison meaningful.
The H-arm itself does not determine the value of the unknown impedance. Its main function is to supply the microwave energy and divide it equally between the two collinear branches. The impedance information is obtained from the way the two branches modify the incident signals and from the adjustment required to bring their responses into the condition necessary for cancellation at the E-arm.
1.b. Connection of the Null Detector to the E-Arm
The null detector is connected to the E-arm because the E-arm provides the difference-mode response of the E-H Plane junction. When signals return from the two collinear branches, they are combined at the junction, and the resulting difference component appears at the E-arm. If the two branch responses are not properly balanced, a residual signal is produced at the E-arm. The null detector detects this residual signal and therefore indicates that the bridge is not yet balanced.
As the known reference branch is adjusted, the amplitude and phase of its response change relative to the response from the unknown branch. The signal at the E-arm consequently changes as the bridge approaches the balanced condition. When the two branch responses satisfy the required cancellation condition, the resultant signal at the E-arm becomes zero under ideal conditions. The null detector then indicates a null. This makes the E-arm an effective detection port because its output directly represents the difference between the relevant signals from the two collinear branches.
1.c. Role of the Two Collinear Arms
The two collinear arms form the two branches of the microwave bridge. One branch contains the unknown impedance, while the other contains a known reference impedance or an adjustable balancing network. When the microwave source excites the H-arm, both branches receive the divided microwave signal. The response of each branch depends on the impedance connected to it, and the returning signals therefore contain information about the corresponding impedance conditions.
If the unknown impedance is not equal to the condition represented by the reference branch, the returning waves will differ in amplitude, phase, or both. These unequal responses produce an imbalance at the difference port. The E-arm therefore provides an indication of the difference between the two branch responses. By adjusting the known branch until the difference disappears, the unknown impedance can be related to the known reference condition.
The two collinear arms are consequently essential to the bridge operation because they provide the paths through which the unknown and reference conditions are compared. The H-arm supplies the common excitation, the collinear arms provide the impedance-dependent paths, and the E-arm detects the resulting difference. Together, these four ports form a microwave bridge capable of determining an unknown impedance through a null measurement.
2. Working Principle of Impedance Measurement Using the E-H Plane Junction
The impedance-measurement process begins when the microwave source supplies a signal to the H-arm. Because the H-arm is a sum port, the input signal is divided equally between the two collinear arms. The two signals initially have the same amplitude and phase, but after entering the measurement branches they are modified according to the impedances connected to those branches. The unknown impedance produces a particular reflected response, while the reference branch produces a response determined by its known or adjustable impedance. These returning signals are then brought back to the E-H Plane junction for comparison.
If the bridge is initially unbalanced, the returning signals do not satisfy the required cancellation condition at the E-arm. A resultant signal therefore reaches the null detector. The operator then adjusts the known reference condition so that the response of the reference branch changes relative to that of the unknown branch. This adjustment continues until the signal detected at the E-arm becomes zero or reaches its minimum value. The corresponding condition is called the balance or null condition of the microwave bridge.
At the null condition, the relevant signal components from the two branches cancel at the E-arm. This means that the two branch responses have reached the amplitude and phase relationship required by the difference-port operation of the E-H Plane junction. Since the reference branch is known, the condition required to obtain the null can be used to determine the unknown impedance. The measurement therefore depends on comparing the unknown branch with a controlled and known reference rather than attempting to measure the unknown impedance directly.
2.a. Unbalanced Condition
When the bridge is unbalanced, the two collinear branches produce unequal responses. The difference between these responses results in a nonzero signal at the E-arm. The null detector therefore registers a measurable output. The presence of this output indicates that the known reference branch has not yet been adjusted to the condition required for cancellation. The direction and magnitude of the adjustment depend on the particular bridge arrangement and the difference between the unknown and reference impedance conditions.
The unbalanced condition is therefore useful rather than undesirable because it provides the information needed to guide the adjustment process. As long as the detector indicates a nonzero signal, the two branches have not reached the required relationship. The reference branch is varied while monitoring the detector until the output decreases toward the null condition.
2.b. Balanced or Null Condition
The bridge becomes balanced when the relevant signals from the two collinear branches cancel at the E-arm. Under ideal conditions, the null detector then indicates zero output. The cancellation occurs because the two branch responses have the required amplitude and phase relationship for the difference-mode operation of the E-H Plane junction. Since the response of the unknown branch depends on the unknown impedance, the balancing condition establishes a relationship between that impedance and the known reference condition.
The null condition is particularly useful in microwave measurement because it provides a precise operating point. Rather than depending entirely on the accuracy of an absolute power measurement, the system identifies a condition at which the detector response reaches zero or a minimum. The measured impedance can then be determined from the known settings and parameters of the bridge at this balanced condition.
3. Role of E-Arm and H-Arm Properties in Impedance Measurement
The successful operation of the E-H Plane junction as an impedance-measurement bridge depends directly on the complementary properties of its E-arm and H-arm. The H-arm provides the sum-mode excitation required to distribute the microwave source signal equally between the two collinear arms. The E-arm provides the difference-mode detection required to observe the imbalance between the two branches. These two properties allow the same junction to perform both the excitation and comparison functions required by the measurement system.
When the signal is applied to the H-arm, the two collinear arms receive equal-amplitude signals with the same phase. This in-phase behavior establishes the initial reference relationship between the two bridge branches. When the returning waves are combined at the E-arm, their relative amplitudes and phases determine whether a residual difference signal exists. If the signals satisfy the appropriate cancellation condition, the E-arm output becomes zero. If they do not, a residual signal is detected. Therefore, the measurement is based on the interaction between the H-arm sum characteristic and the E-arm difference characteristic.
The phase relationship is especially important when measuring complex impedance. An impedance may introduce both magnitude and phase changes into the reflected wave. Consequently, two branches can have similar signal amplitudes but still fail to produce a null because their phases are different. The balancing process must account for both amplitude and phase so that the signals cancel correctly at the E-arm. This is why the E-H Plane junction is capable of providing a phase-sensitive microwave measurement rather than simply acting as a power divider.
4. Impedance Measurement Through Bridge Balancing
The complete measurement process can be summarized as a controlled bridge-balancing operation. First, the microwave source is connected to the H-arm and supplies the required microwave excitation. The H-arm divides this excitation between the two collinear arms. The two signals then travel through the branches containing the unknown impedance and the known reference condition. Because the impedance conditions are generally different at the beginning of the measurement, the returning signals will also be different. These signals combine at the E-H Plane junction, producing a residual difference signal at the E-arm that is observed by the null detector.
Next, the known branch is adjusted while observing the null detector. The purpose of this adjustment is to make the response of the known branch correspond appropriately with the response of the unknown branch. As the bridge approaches balance, the difference signal at the E-arm becomes smaller. At the correct setting, the detector reaches a null or minimum response, indicating that the required cancellation condition has been achieved. The settings of the known branch at this point provide the basis for determining the unknown impedance.
The method can therefore be represented as a sequence of microwave operations: the H-arm supplies the source signal, the collinear arms form the measurement branches, the unknown impedance modifies one branch response, the reference branch provides the adjustable comparison, and the E-arm produces the difference signal that is observed by the null detector. When the detector reaches the null condition, the bridge is balanced and the unknown impedance can be evaluated.
Advantages of E-H Plane Junction for Impedance Measurement
The use of an E-H Plane junction for impedance measurement provides several useful characteristics. First, the junction provides equal signal division through the H-arm, allowing the two measurement branches to be excited under controlled conditions. Second, the E-arm provides a difference-mode output, making it possible to detect even a small imbalance between the two branches. Third, the use of a null detector provides a clearly identifiable balance point. Finally, because microwave impedance affects both amplitude and phase, the phase-sensitive operation of the Hybrid Tee allows the measurement arrangement to account for the complete microwave response of the impedance.
The main functions of the four ports in the impedance-measurement arrangement can therefore be summarized as follows:
H-arm: The H-arm is connected to the microwave source and provides equal-amplitude in-phase excitation to the two collinear arms.
Collinear arms: The collinear arms form the two branches of the microwave bridge, with one branch associated with the unknown impedance and the other with the known reference or balancing arrangement.
E-arm: The E-arm acts as the difference port and produces the resultant signal associated with the imbalance between the two measurement branches.
Null detector: The null detector observes the E-arm output and identifies the condition at which the bridge becomes balanced.
Overall Operation of the E-H Plane Junction as an Impedance Measurement Device
The E-H Plane junction provides a convenient microwave method for measuring an unknown impedance by combining equal signal division, phase-sensitive comparison, and null detection in a single passive junction. The microwave source connected to the H-arm establishes equal-amplitude in-phase excitation at the two collinear arms. The unknown and reference conditions modify the signals travelling through their respective branches, causing the returning waves to differ in amplitude and phase. These waves are then combined at the junction, and the resulting difference signal appears at the E-arm. The null detector connected to the E-arm indicates the degree of imbalance and allows the bridge to be adjusted toward the required cancellation condition.
When the bridge reaches the balanced condition, the relevant signals cancel at the E-arm and the null detector indicates zero or minimum response. The known reference condition at this point can be used to determine the unknown impedance. Hence, the impedance-measurement application of the E-H Plane junction is based fundamentally on the H-arm sum-port characteristic, E-arm difference-port characteristic, equal power division, amplitude and phase comparison, and bridge balancing principle. This makes the E-H Plane junction an important microwave component for impedance measurement and demonstrates a practical application of the fundamental properties of a Magic Tee.