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.
Figure 2.17 RF performance of a directional bridge.
Bridges of this type have been used successfully up to 27 GHz.
2.2.4.2 Directional Couplers
Directional couplers are more often used in higher‐microwave frequency ranges because of the difficulty of maintaining good bridge performance at high frequencies. Directional coupler design is a broad topic, and much literature has been devoted to structures that can be used as couplers. However, for use in VNAs, there are some particular characteristics that are critical. In general, commercial directional‐couplers are designed to maintain a flat coupling factor over their bandwidth, and the bandwidth is limited by this coupling factor. Couplers used for VNA reflectometers require wide bandwidths, so rather than a flat response, they are often designed with an equal‐ripple or Chebyshev response. Ripple in the loss or coupling factor is not much concern in a modern VNA, where calibration techniques can remove almost any frequency response error. Isolation is an important criteria in VNA couplers. One attribute about directional‐couplers that distinguish them from bridges is that they are ideally lossless devices such that all the power applied is either coupled (to the coupled port or the internal load) or transmitted through the coupler. The relationship between insertion loss and coupling factor is
(2.8)
Directional couplers typically come in one of three forms: waveguide couplers, microstrip couplers, and stripline couplers.
Waveguide couplers are most common at mm‐wave frequencies but have the inherent limitation of narrowband operation due to the narrowband nature of waveguides. The structure of waveguide couplers is a 4‐port device with the main arm connected in such a way as to have irises (or holes) to a second waveguide. The second waveguide can have two ports or one port internally terminated. The nature of the coupler is symmetrical. In theory either port can be the coupled port; in practice a load is often embedded in the coupled arm. Because of the fundamental function of a waveguide coupler, the forward coupled wave comes out of the waveguide port nearest the test port. This often causes confusion in the symbols used.
A microstrip or stripline coupler uses a different electric‐magnetic (EM) configuration to perform coupling, and the coupled arm of these couplers is the one farthest from the test port. Microstrip couplers often suffer from the fact that there is some dispersion in microstrip lines, and since the even‐ and odd‐mode waves in the coupled lines experience different effective dielectric constants, they will have different velocities of propagation. This makes it more difficult to create microstrip couplers with good isolation. For this reason, many VNA couplers are in the form of stripline (or slabline, which is similar to stripline but with a rectangular center conductor thickness), suspended in air. These couplers are designed to have very stable coupling and isolation factors. For a VNA, it is not so important what the exact directivity is, as long as it is completely stable. Figure 2.18 shows an example of a directional‐coupler used in VNAs. The test port connector is one attribute that differentiates this from a commercially available directional‐coupler that might be used as component in a different system. This connector is designed to be firmly mounted to the VNA front panel and withstand numerous connections and reconnections. This coupler has an integrated load and so exposes only three ports.
Figure 2.18 A directional coupler used in VNAs.
2.2.4.3 1+Gamma
Another proposed reflectometer structure is a 1+gamma structure, whose name comes from the block‐diagram architecture, shown in Figure 2.19. As the name implies, the signal at the b1 receiver is a combination of the incident (a1) and reflected (gamma) signal.
Figure 2.19 Block diagram of a 1+gamma reflectometer.
In this configuration, the signal in the test or b1 receiver never goes to zero; rather, it is minimum with a short, maximum with an open, and nominal 1 when there is a load attached. Also, the signal variation between an open and short is about 14 dB less than that for a bridge or directional‐coupler. Put another way, the reflection gain of the 1+gamma bridge is lower than for a directional‐coupler or bridge. Consider the Smith chart in Figure 2.20; an open, short, and load (all non‐ideal with fringing capacitance and series inductance) are shown for each on a 1+gamma reflectometer.
Figure 2.20 Smith chart showing reflections of a 1+gamma bridge with an open, short, and load.
The value of attenuation in the reference channel is adjusted to set the value of the open circuit reflection to 1. For a directional‐coupler, the load gives a zero reflection (ideally), and the short gives a −1
