The vector network analyzer (VNA) is an essential tool for measuring the complex impedance of a circuit at a given frequency. The basic principles of operation are quite simple. So, by following the ideas presented here and adding a few op amps and resistors, it’s easy to design and construct a useful analyzer that can operate from dc to a few megahertz.
Broadband network analyzers are typically built around a VSWR bridge. VSWR stands for voltage standing-wave ratio. The topology of the VSWR bridge is similar to that of the Wheatstone bridge. When the signal VSOURCE is applied to the bridge, a portion of the signal appears at the terminals of the device under test (DUT) as an incident voltage, VINC. If the DUT doesn’t perfectly terminate the bridge in the system impedance, then a reflected voltage (VREF) will also appear at the terminals of the DUT. Signals that are proportional to the incident and reflected voltages appear across different resistors within the bridge. The amplitude and phase of these signals is then compared to determine the impedance of the DUT at the signal frequency (see the figure).
Amplifiers A1 and A2 act as active baluns to transform the balanced signals appearing across the resistors in the bridge to more useful singleended results. The gains of A1 and A2 are unimportant as long as they are equal. To maximize the operational bandwidth of the analyzer, A1 and A2 should have low gain (AV ˜ 1) and be identical in configuration. At higher frequencies, the signal source amplitude should be limited to a few hundred millivolts peak-to-peak to reduce the effects of the amplifiers’ slew rate. For low values of RO, simple diff- amps may be used. For higher values of RO, instrumentation amps must be used to prevent loading down the bridge.
The resistor in the upper left portion of the bridge is centertapped to properly scale the incident voltage signal. The impedance of the DUT is found by first determining the voltage reflection coefficient, G. The impedance of the network then is:
ZDUT = RO(1 + G)/(1 - G)
where G = VREF/VINC.
For a passive DUT, |VREF| = |VINC|, so |G| = between VREF and VINC whenever the DUT has a reactive component.
This arithmetic is tedious but it’s easily automated using a programmable calculator or a spreadsheet. To simplify calculations, assume that VINC is the zero-phase reference. Some other useful quantities can be determined from G. The retum loss and the VSWR of the DUT are common figures of merit. A well matched circuit will have high return loss and a VSWR near unity:
RL = -20log|G|
VSWR = (1 + |G|)/(1 - |G|)
The impedance measurement is easily done using a function generator for the signal source and an oscilloscope to measure the magnitudes and phases of VREF and VINC. These are ratiometric measurements as long as A1 and A2 are identical. The gain and phase response characteristics of the amplifiers cancel when computing G!
The table shows just a few applications of the VNA versus system impedance.