source‐match. If there is mismatch before the directional device, it will have no effect on its directional characteristics (directivity or isolation). However, any mismatch after the directional device, such as in a test port cable or fixture, will contribute equally to mismatch and degradation of directivity, as described in Section 1.10.
2.2.4.1 RF Directional Bridges
Most RF VNAs make use of a directional bridge, which has the important characteristic of maintaining good coupling and isolation over very wide frequency ranges and at very low frequencies. While the most common implementation of a bridge is a balanced Wheatstone bridge, this simple implementation can be modified to create a component that has characteristics similar to a directional‐coupler, but with much wider frequency range and low frequency of operation. A bridge is often used in metrology applications where balance in a DC resistive path provides a measure of some quantity such as the power absorbed by a load (see Section 1.15). To understand how these bridges can be configured as directional‐couplers, with low loss and high isolation, consider the diagram in Figure 2.12, which is a common representation of a Wheatstone bridge.
Figure 2.12 Schematic of a directional bridge.
In this configuration, the signal from the source is applied across the top and bottom of the bridge, and if the ratio of R1/R2 is equal to R4/R3, the net voltage across Rdet (which in a common bridge represents the meter movement) will be zero, and no current will flow through the detector.
In a thermistor, all the resistors are 50 Ω, and one of them represents the RF input of the power sensor, typically R3. A DC signal is applied from the source across the bridge, and the imbalance is measured as the voltage difference across the Rdet resistor. In an RF bridge it is desired to isolate the bottom node of the bridge from ground, and so a transformer is added for this purpose, as shown in Figure 2.13. This 1:1 transformer performs the function of a BALanced‐UNbalanced transformer (or balun), changing the unbalanced (or grounded) source into a balanced signal across the bridge. Doing this allows grounding a different leg of the bridge, which as will be seen is key to making a bridge act as a directional‐coupler.
Figure 2.13 Adding a transformer between the source and the bridge.
From this modification, the RF implementation of the bridge can be better understood. Since the low side of the detector is now ground, the resistor represented by Rdet and R4 can be replaced with transmission line structures of similar impedances, representing the RF ports of the directional bridge, as shown in Figure 2.14. In this figure, the Rdet resistor is replaced with the coupled port of the bridge, and one can see that the RF energy flowing from the source appears equally at both the center conductor and the ground of isolated port.
Figure 2.14 Replacing bridge elements with RF ports.
However, since the RF current appears at the test port, relative to ground, a portion of the RF signal will appear across R4; the relative value of the voltage on R4 to Vs/2 is the insertion loss of the directional bridge. If the bridge uses equal resistors, then R1, R2, R3, and R4 as well as Rs are all 50 Ω. With these values, it is easy to see that Vs is applied equally to R1 and R2, as well as R3 and R4, so that the voltage across R4 is one‐fourth the source voltage. Therefore, the loss of an equal resistor balanced bridge is one‐half voltage applied at the bridge input, or −6 dB. In general, the insertion loss of a bridge, where RS = R4 = Z0 is
(2.4)
From this description we can see that in the case where the bridge is terminated in Z0, there is no signal in the isolated port, demonstrating that this bridge isolates the incident signal. The first criteria of a directional device is satisfied. The second criteria is that the bridge does respond to the reflection signal from the test port. To understand how that occurs, it is useful to redraw the bridge, bringing the ground point of the test port down to the bottom of a redrawn circuit, as shown in Figure 2.15.
Figure 2.15 A bridge redrawn to show the coupling factor.
In this drawing, the source has been moved from the input to the output, but the bridge circuit is topologically identical to the previous figure. When driven from the test port (or when measuring a reflected signal), the isolated arm becomes the coupled arm, and the coupling factor of the coupled arm can be computed as
(2.5)
For the case of an equal resistor bridge, the coupling factor is equal to the loss, −6 dB. If R1 is not equal to Z0, R3 can be computed as
(2.6)
Note that the loss is directly proportional to the coupling as
(2.7)
For RF VNAs, it is common to use a directional bridge in the test set. Directional bridges of this type have been used since the 1970s, and an example of such a bridge used in the HP 8753B is shown in Figure 2.16. This bridge has been modified to have an unequal coupling and loss, so the insertion loss is lower than normal (around −1.5 dB), and the coupling is higher than normal (around −16 dB) for a Wheatstone bridge.
Figure 2.16 An example of a directional bridge from the HP 8753B.
The RF performance of such a microwave bridge is shown in Figure 2.17. The insertion loss increases with frequency due to the loss of the coax balun and increased coupling due to parasitic series inductance in R3. This same inductance causes a degradation of directivity in the bridge as frequency increases. Bridges are inherently lossy structures, where some of the power is absorbed by the resistive elements in the bridge. The power absorbed by the bridge is equal to the insertion loss of the bridge minus the power coupled to the coupled port.