Steven Dunbar
Inovonics Corp., 2100 Central Ave., Boulder, CO 80301; (303) 939-9336; sdunbar@inovonics.com
May 29, 2000 • ELECTRONIC DESIGNから引用
T
he 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, Γ. The impedance of the network then is:
ZDUT = RO(1 + Γ)/(1 − Γ)
where Γ = VREF/VINC.
For a passive DUT, |VREF| ≤
|VINC|, so |Γ| ≤ 1. In general, Γ
and ZDUT are complex numbers
because a phase difference exists 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 Γ. 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|Γ|
VSWR = (1 + |Γ|)/(1 − |Γ|)
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 Γ!
The table shows just a few applications of the VNA versus
system impedance.
