target="_blank" rel="nofollow" href="#ulink_28af5bf0-1b0c-50c5-9dff-ec08d1f6aa41">Figure 2.6, where a two‐resistor power splitter is used, and the source impedance is also 50 Ω.
Figure 2.6 Simplified diagram of source power match.
From the test port one sees a series of 50 Ω resistance (of the splitter), behind which is the 50 Ω source impedance in parallel with 100 Ω (50 Ω from the splitter, 50 Ω from the reference receiver, in series), to generate a power match of
(2.1)
as the Thevenin equivalent impedance. From this it is clear that the for the two‐resistor splitter case, even in an ideal case the power source‐match cannot be Z0.
In the case where a directional‐coupler is used in the reference channel, the nominal match may be much closer to Z0. The result of this non‐50 Ω equivalent power source‐match is that when the DUT is not matched, there will be a reflected signal that, while it will be detected by the reference channel and thus compensated for in gain measurements, will cause the a1 wave to vary from the value one sees when the port is terminated in 50 Ω and thus cause error or ripple in the drive power to the DUT, as illustrated in Figure 2.7. The figure shows, in the dark trace, the incident power at a1 for a load at the test port. It is not perfectly flat because of other mismatches in the system after the reference coupler. The light trace shows the result of an open at the test port. This large ripple is because of the poor power source‐match and generates an error in the incident signal of nearly 1 dB. Since this is power measured at the a1 receiver, it is related to the ripple in the output power, but other loss or reflections between the reference splitter and the test port can affect the output power. Other reflections past the reference splitter will add to the power source‐match but are not represented in the a1 measurement. In the case of a linear device, which S‐parameters presume, this is of no consequence; but in the case of non‐linear devices, such as amplifiers in compression, this will directly affect the reported output power. In such a case, the drive power from the VNA can be higher or lower than the displayed power setting, so the amplifier will be further, or lesser, in compression and the power reported will be in error if based on the input drive level.
Figure 2.7 Measured incident power into a load termination and an open termination for a VNA with a coupler in the reference channel.
The power source‐match is quite difficult to determine as it is apparent only when there is a mismatch applied at the test port. In essence, one must vary the impedance applied to the test port and measure the change in power coming out of the drive port to infer the power source‐match; it cannot be directly measured. By using a “long‐line” technique, a line‐stretcher, a sliding mismatch, or an impedance tuner as a termination of the test port, and adding a coupler to sample the incident wave (shown in Figure 2.8), one can determine the power source‐match from a series of measurements, where the line stretcher or tuner is changed.
Figure 2.8 Block diagram for measuring power source‐match.
A line‐stretcher is a transmission line structure, usually stripline, that allows the length of the transmission line to be varied. These are sometimes called trombone‐lines because the center conductor is constructed as a trombone‐like slider. An example of one is shown in Figure 2.9.
Figure 2.9 A line stretcher used for match measurements.
The traces shown in Figure 2.10 measure the a1 wave from the test port output by adding an external coupler and routing the coupled arm to the b2 receiver. The main arm of the coupler is connected to a power meter, and the power is set to obtain −10 dBm; then the b2 receiver is calibrated to this output power. Next the power meter is removed, and a long line terminated in full reflection (short or open) is put in its place. The ripple on the trace is an indication of the power mismatch. Though not shown, in this case the effective source‐match (or ratio source‐match) is good, but the output power has ripple related to the power mismatch. When the line is terminated with a short or open, the peak‐to‐peak ripple is exactly the voltage standing‐wave‐ratio (VSWR) of the power source‐match. The upper trace is a measurement of a system with a power splitter used for the reference signal separator; the lower trace shows the same measurement, but this time the power splitter is replaced with a directional‐coupler for the reference‐channel signal separation. Clearly, there is an improvement in the power source‐match using the coupler.
Figure 2.10 Measurement of long line indicating power source‐match using an external coupler terminated in a short: a two‐resistor power splitter (upper) and a trace for a coupler in the reference path (lower).
At any frequency, the VSWR of the power source‐match can be determined from this response; the envelope of the response can be used directly, or the line stretcher may be adjusted to obtain a peak and valley at any frequency of interest, from which the power source‐match is computed as
(2.2)
where VSWR is the peak‐to‐peak ripple in dB found at the output of the monitoring coupler and LCM is the loss in the main arm of the monitoring coupler. In the upper trace of the previous example, the p‐p ripple at low frequency is about 3.0 dB, and the mainline loss of the external coupler is about 1.6 dB, so the power source‐match is
(2.3)
This is almost exactly the power match expected from a 50 Ω splitter (83.3 Ω or −12.05 dB). The lower trace shows a power source‐match for a directional‐coupler of around −21.6 dB at low frequencies, and −18 dB at higher frequencies.
Extracting the effective match from a mismatch ripple is a technique that will be useful for many other analyses in component measurement. An alternative test method uses a mismatch pad connected to another
