A Low Cost RF Impedance Analyzer
saved. These can be called up from the
main screen. Calibration data is saved
in a file RFinit upon exit. My data is in
the original file so you can see my
resistor values, voltages, and calibration results. When you save your data,
it will just overwrite the old data.
There is a quirk with the TVM calculation as alluded to earlier whereby
the result of the cosine calculation may
produce a value greater than one. This
happens only with resistors where the
phase angle is supposed to be zero.
Slight inaccuracies in measurement are
the cause of the problem. To keep you
informed of this situation, the results of
the cosine calculation are shown on the
calibration screen. Don’t be alarmed if
you see cosines above one. Hopefully,
they will be very close to one and won’t
affect the program results substantially.
This is just a peculiarity of this method.
On the main screen, the box with
the offending angle (cosine greater than
one) will be highlighted in a red color.
Since the error is often small and occurs
mainly with resistors, the program will
substitute a suitable small angle. In case
you don’t like the value chosen, you
have the option of assuming the angle
to be zero. Also, if you don’t like the calibration values found by the computer
algorithm, you can try to adjust them
manually. The resulting error is shown
on the screen as a guide. I have tried
several times to “best” the program but
have been unsuccessful. It seems to do
a good job, though.
The calibrate algorithm is straightforward. An error criterion shown
below is evaluated by a brute force
search for the minimum of “Error.” Each
diode parameter is varied separately in
tiny increments and “Error” calculated.
error or the difference between the calculated Z and the calibration resistor.
The second term is the error between
the calculated cosine and the value of
one, which it would be for a resistor.
The weighting factor W(i) is set to
10,000 since the cosine changes are
small and change slowly near one.
The algorithm stops when it can
find no variation in the diode parameter that reduces “Error” any further.
These parameters are shown on the
screen. This doesn’t necessarily mean
the lowest error is found. There may
be other local minima due to the nonlinear property of the diode and there
is a possibility that the algorithm has
gotten stuck on one of these. But as
noted above, I haven’t been able to
find a better minimum in my testing.
Determining the Sign
of the Impedance Angle
We saw previously from Equation 4
that the analyzer cannot determine the
sign of the impedance angle, θ, so let’s
explore other methods of finding it.
For lumped parameter components like capacitors and inductors, the
sign is obvious since capacitive reactance is negative while inductive reactance is positive, as seen in Figure 1.
This leads to the following simple rule
of thumb for lumped parameter parts.
If Z increases with increasing
frequency, then the load is inductive
and θ > 0. While ifZ decreases with
increasing frequency, then the load is
capacitive and θ < 0. So, by slightly
changing the frequency and looking
at the change of impedance, we can
find the sign. This rule works for RC
and RL circuits and even simple RLC
circuits. An easy way of doing this is to
monitor Vz. For example, if Vz is
decreasing as frequency increases, the load is capacitive.
If we look at the input impedance of a transmission line with a
load attached, the above rule is not
strictly obeyed. It may be obeyed at
some frequencies but not at others.
There is a special case where it is
obeyed — that of a zero resistance load
— an example of which will be dis-
cussed later on. But in general, the rule
does not hold, particularly if the load is
complex. So, if you are not sure of the
nature of the load attached to the transmission line, do not use the above rule.
There are other ways of finding
the sign. It is an easy matter to add a
small amount of reactance in series
with the input and observe the angle
change. For example, if you added
some capacitive reactance and the
angle increases, then the input is
capacitive and the angle is negative.
If you know the length and type of
transmission line and the type of load
(such as an antenna), you can make
some good estimates of the sign. For
example, if the load is an 80-meter dipole
of known resonant frequency, you can
expect the antenna to be capacitive just
below resonance and inductive above
resonance. Then using a program like
AC6LA’s Transmission Line Details (TLD),
you can calculate an estimate of the
input impedance which should help
determine the sign. TLD is designed for
Windows and easily found on the web
[ 3]. Let’s look at some other applications.
Applications of an
i or ∑= 4 Err = (Zmag (i ) − Rcal (i )) 2 + W (i )(cos(i ) −1) 2
Here Zmag(i) is the calculated magnitude of Z, Rcal(i) is the calibration
resistor, W(i) is a weighting factor on the
cosine error, and “i” is the first through
fourth calibration resistor. The first term
in the sum is the error due to magnitude
Uses for an impedance analyzer
abound. And if the accuracy requirements aren’t extreme, this unit can
produce good results. It can be used to
check components like inductors and
capacitors at their operating frequency,
measure the input impedance of a
matching network, and even measure
the impedance of an antenna. Coaxial
cable transmission lines — which often
seem mysterious to many — can be
investigated easily with this analyzer.
First, let’s consider a simple RC circuit consisting of a 100.3 ohm resistor
and a 527 pF mica capacitor connected in parallel. The component values
were individually measured at an
audio frequency of 1 kHz. I connected
them in parallel as the unknown Z for
the analyzer, read the three voltages at
3. 5 MHz, 7.0 MHz, and 10 MHz, and
entered the data into the program.
Figure 10 shows a comparison of the
measured and theoretical values.
February 2008 45