EXPERIMENT-2
AIM: Microwave Measurement Parameters:
Frequency
measurement:
Counters
and pre-scalers for direct frequency measurement in terms of a quartz crystal reference
oscillator are often used at lower frequencies, but they give up currently at
frequencies above about 10GHz. An alternative is to measure the wavelength of
microwaves and calculate the frequency from the relationship (frequency) times
(wavelength) = wave velocity. Of course, the direct frequency counter will give
a far more accurate indication of frequency. For many purposes the 1% accuracy
of a wavelength measurement suffices.
Signal
strength measurement
The 10
GHz microwave signal in the waveguide is "chopped" by the PIN
modulator at a frequency of 1 kHz (audio) and the square wave which does this
is provided by the bench power supply.
The
detector diodes in the mounts on the wavemeter and slotted line rectify and
filter this 10GHz AM signal and return a 1kHz square wave which you can observe
directly on the oscilloscope. They are actually being used as "envelope
detectors" as is the detector diode in your AM radio.
The
VSWR indicator is a 1kHz tuned audio amplifier with 70dB dynamic range at
least, and a calibrated attenuator sets its gain. The meter measures the size
of the audio signal at 1kHz.
Since the detectors are
"square law" their output voltage is proportional to the square of
the microwave signal voltage. Regarded as a linear meter then, the VSWR
indicator gives a deflection proportional to the POWER of the microwave signal
(V*V/Zo). That is the reason for the curious calibration on the VSWR scales.
Half scale deflection
on the VSWR meter therefore represents a microwave voltage of 1/sqrt(2) or
0.707 of that corresponding to full scale deflection.
Moreover, the VSWR
meter is calibrated "backwards" in that one sets the voltage maximum
at full scale deflection, then reads the VSWR from the voltage minimum. Thus
the calibration point at half scale deflection is actually 1/0.707 or 1.414
VSWR. Check this. At 1/10 of full scale deflection the VSWR calibration point
is sqrt(10) or 3.16. At this point one increases the gain by a factor of 10
with the main attenuator adjustment, and reads the VSWR scale from 3.16 to 10
on the other half of the VSWR scale. Get a demonstrator to show you how if this
isn't yet clear.
Note that the gain dB
scales and the attenuator on the VSWR indicator correspond to POWER of the
microwave signal, not to POWER of the 1kHz audio input.
Measurements of impedance and
reflection coefficient.
A visit to your
favourite microwave book shows that a measurement of the standing wave ratio
alone is sufficient to determine the magnitude, or modulus, of the complex
reflection coefficient. In turn this gives the return loss from a load
directly. The standing wave ratio may be measured directly using a travelling
signal strength probe in a slotted line. The slot in waveguide is cut so that
it does not cut any of the current flow in the inside surface of the guide
wall. It therefore does not disturb the field pattern and does not radiate and
contribute to the loss. In the X band waveguide slotted lines in our lab, there
is a ferrite fringing collar which additionally confines the energy to the
guide.
To determine the phase
of the reflection coefficient we need to find out the position of a standing
wave minimum with respect to a "reference plane". The procedure is as
follows:-
First, measure the
guide wavelength, and record it with its associated accuracy estimate.
Second, find the
position of a standing wave minimum for the load being measured, in terms of
the arbitrary scale graduations of the vernier scale.
Third, replace the load
with a short to establish a reference plane at the load position, and measure
the closest minimum (which will be a deep null) in terms of the arbitrary scale
graduations of the vernier scale. Express the distance between the measurement
for the load and the short as a fraction of a guide wavelength, and note if the
short measurement has moved "towards the generator" or "towards
the load". The distance will always be less than 1/4 guide wavelength
towards the nearest minimum.
Fourth, locate the r
> 1 line on the SMITH chart and set your dividers so that they are on the
centre of the chart at one end, and on the measured VSWR at the other along the
r > 1 line. (That is, if VSWR = 1.7, find the value r = 1.7).
Fifth, locate the short
circuit point on the SMITH chart at which r = 0, and x = 0, and count round
towards the generator or load the fraction of a guide wavelength determined by
the position of the minimum.
Well done. If you plot
the point out from the centre of the SMITH chart a distance "VSWR"
and round as indicated you will be able to read off the normalised load
impedance in terms of the line or guide characteristic impedance. The fraction
of distance out from centre to rim of the SMITH chart represents the modulus of
the reflection coefficient [mod(gamma)] and the angle round from the r>1
line in degrees represents the phase angle of the reflection coefficient
[arg(gamma)].
Network
analysers.
A network analyser makes measurements of complex
reflection coefficients on 2-port microwave networks. In addition, it can make
measurements of the complex amplitude ratio between the outgoing wave on one
port and the incoming wave on the other. There are thus four possible complex
amplitude ratios which can be measured. If we designate the two ports 1 and 2
respectively, these ratios may be written s11 s12 s21 s22. These are the four "s-parameters" or "scattering
parameters" for the network. Together they may be assembled into a matrix
called the "s-matrix" or "scattering matrix".
The network analyser works on a different
principle to the slotted line. It forms sums and differences of the port
currents and voltages, by using a cunning bridge arrangement. The phase angles
are found by using synchronous detection having in-phase and quadrature
components. From the measured voltage and currents it determines the incoming
and outgoing wave amplitudes. As we recall from elsewhere
in the notes, V+ = (V + ZoI)/2 and V- = (V - ZoI)/2.
Network analysers can
be automated and controlled by computer, and make measurements at a series of
different frequencies derived from a computer controlled master oscillator.
They then plot the s-parameters against frequency, either on a SMITH chart or
directly.
The important
experimental technique to the use of a network analyser lies in the calibration
procedure. It is usual to present the analyser with known scattering events,
from matched terminations and short circuits at known places. It can then
adjust its presentation of s-parameters for imperfections in the transmission lines
connecting the analyser to the network, so that the user never has to consider
the errors directly providing he/she can trust the calibration procedure. It is
even possible to calibrate out the effects of intervening transmission
components, such as chip packages, and measure the "bare"
s-parameters of a chip at reference planes on-chip.
S-Parameter Simulation Controller
The S-Parameter controller
is used to define the signal-wave response of
an n-port
electrical
element at a given frequency. It is a type of
small-signal
AC simulation that is most
commonly used to characterize a passive RF
component and establish
the small-signal characteristics
of a device at a specific bias
and temperature.
·
Obtain the scattering parameters (S-parameters)
of a component or circuit, and convert the parameters to Y- or Z-parameters.
·
Plot, for example, the variations in
swept-frequency S-parameters with respect to another changing variable.
·
Simulate group delay.
·
Simulate linear noise.
·
Simulate the effects of frequency conversion on
small-signal
·
S-parameters in a circuit employing a mixer.
Smith Chart
- When the need arises
to look at input impedances
and/or reflection
coefficients
as complex quantities,
the Smith chart can
be very helpful.
- When frequency is
swept, as in S-parameters simulations, we get
a locus of points
in the Smith chart to consider. The
markers can be useful then for evaluating impedance
and reflection
values at a particular frequency of interest
In the Schematic window of ADS, choose Tools
> Smith Chart.
The Control window opens.
Or, you can
choose one of these paths
from the Design
Guide menu:
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