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2.2.4.3 1+Gamma

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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 reflection. For the 1+gamma bridge, the open is also 1, but the short is +0.6, and the load is +0.75; thus, the difference between the open and the short moves from 2 to only 0.4. These reflections are mapped to the full Smith chart through the error correction math, in such a way that the values from the reflections, and any instability, are multiplied by 5. Also, since the load condition has a large signal in the b1 receiver, any instability in that signal is apparent as a directivity error, which is also multiplied by 5. In theory, if directivity is defined as the average of the open/short response relative to the load response, then the directivity of a 1+gamma reflectometer is about 0 dB (remember that directivity for a coupler or bridge is always positive, often 20 dB or more).

Theoretically, any directivity error can be corrected for by a calibration, but in practice, certain unstable errors can cause uncorrectable errors when the directivity is poor. Thus, 1+gamma structures have largely disappeared from use. Also, this same multiplying effect causes any slight drift in the test port cable to cause a considerable change in the measured reflection coefficient, after calibration.

Handbook of Microwave Component Measurements

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