S parameters
Scattering parameters describe a network by what it does to waves entering and leaving its ports — which is the natural description at RF, where you cannot easily measure voltage and current directly.
What do the subscripts of S parameters represent?
The port or ports at which measurements are made.
The convention is S(out, in) — the first subscript is where the signal comes out, the second is where it went in.
| Parameter | Meaning |
|---|---|
| S11 | input port return loss or reflection coefficient |
| S21 | forward gain (or insertion loss) |
| S12 | reverse gain — isolation |
| S22 | output port return loss |
S21 is in at port 1, out at port 2 — forward transmission. S11 is in at port 1, back out at port 1 — reflection. Once you have the ordering, the whole set follows.
For an amateur, S11 is what an antenna analyser reports as SWR, and S21 is what you measure to characterise a filter.
Vector network analysers
What three test loads are used to calibrate an RF vector network analyzer?
Short circuit, open circuit, and 50 ohms.
Three known loads — the SOL calibration — let the instrument solve for its own errors: cable loss, connector mismatch, directivity. Calibration is done at the end of the cables you will actually use, which is why a NanoVNA must be recalibrated whenever you change test leads.
Which of the following can be measured by a two-port vector network analyzer?
Filter frequency response.
Which of the following can be measured with a vector network analyzer?
All these choices are correct — SWR, filter frequency response, and return loss.
A VNA is the instrument that made serious RF measurement affordable for amateurs. A NanoVNA costs less than a decent multimeter and does what a laboratory instrument did twenty years ago.
Accuracy limits
Which of the following factors most affects the accuracy of a frequency counter?
Time base accuracy.
A counter counts cycles in a known interval, and the whole measurement is only as good as that interval. A counter with eight digits and a poor crystal displays eight digits of which three are meaningful — which is why the GPS-disciplined oscillator from the circuits lesson exists.
What is the significance of voltmeter sensitivity expressed in ohms per volt?
The full scale reading of the voltmeter multiplied by its ohms per volt rating is the input impedance of the voltmeter
An old analogue-meter specification with a live consequence. A 20,000 ohms-per-volt meter on a 10 V range presents 200 kΩ — which visibly loads a high-impedance circuit and gives a low reading. The General track’s “voltmeters have high input impedance” is this, quantified.
Computing absorbed power
How much power is being absorbed by the load when a directional power meter connected between a transmitter and a terminating load reads 100 watts forward power and 25 watts reflected power?
75 watts.
100 − 25 = 75 watts. Simple subtraction, and worth noting what it implies: 25 W is heading back to the transmitter. (For interest, 25/100 reflected corresponds to an SWR of 3:1 — the reflected power fraction is the square of the voltage reflection coefficient, so Γ = 0.5.)
Measuring Q and IMD
Which of the following can be used to determine the Q of a series-tuned circuit?
The bandwidth of the circuit’s frequency response.
Rearranged from BW = f₀/Q: measure the −3 dB bandwidth and the resonant frequency, and Q = f₀/BW. That is a measurement you can make with a signal generator and a detector — or, in one sweep, with a VNA.
Which of the following methods measures intermodulation distortion in an SSB transmitter?
Modulate the transmitter using two AF signals having non-harmonically related frequencies and observe the RF output with a spectrum analyzer.
The two-tone test from the General track, stated in full. Non-harmonically related so the distortion products do not hide under the tones, and a spectrum analyser to see them.
Check yourself
- Your VNA shows S21 falling steeply above 30 MHz on a filter. What have you measured?
- A directional meter reads 200 W forward, 8 W reflected. How much reaches the load?
- Your frequency counter reads 146.520037 MHz. How much of that do you believe?
Answers
- Forward transmission — in at port 1, out at port 2. You have measured the filter’s response, and it is rolling off above 30 MHz.
- 200 − 8 = 192 watts.
- Only as many digits as the time base supports. A counter with an ordinary crystal is good to a few parts per million, so about 146.5200 MHz is honest and the last two digits are decoration.