E4B: Measurement Techniques

E4B covers the accuracy limitations and practical techniques of RF and electronic measurement: frequency counter accuracy and its dependence on time base, voltmeter sensitivity and input impedance, S parameters and vector network analyzers (VNAs), power measurement with forward and reflected readings, determining circuit Q from bandwidth, and the correct method for measuring intermodulation distortion in an SSB transmitter.

These topics require understanding of both what is being measured and what limits measurement accuracy.

Frequency Counter Accuracy

The accuracy of a frequency counter is most affected by time base accuracy. A frequency counter works by counting the number of input signal cycles that occur during a precisely defined time window (called the gate time). The time window is generated by the counter's time base — typically a crystal oscillator or TCXO (temperature-compensated crystal oscillator). If the time base oscillator is inaccurate, the gate time will be wrong, and every frequency measurement will be in error by the same fractional amount as the time base error.

Input attenuator accuracy, decade divider accuracy, and temperature coefficient of the logic circuits are secondary factors that do not dominate the counter's overall accuracy the way time base accuracy does.

Voltmeter Sensitivity and Input Impedance

A voltmeter's sensitivity is expressed in ohms per volt — this is the meter's input impedance normalized to its full-scale voltage range. The significance is that the full-scale reading of the voltmeter multiplied by its ohms per volt rating equals the input impedance of the voltmeter at that range setting.

This matters because a voltmeter with low input impedance will load the circuit under test, drawing current and reducing the measured voltage below the actual circuit voltage. High-sensitivity (high ohms/volt) meters have less loading effect.

S Parameters

S parameters (scattering parameters) are a set of measurements used to characterize two-port RF networks. The subscripts identify the ports at which measurements are made — the first subscript is the output port, and the second subscript is the input port.

The first subscript always indicates where the signal is measured (the output port for transmission parameters), and the second subscript indicates where the signal is applied (the input port).

VNA Calibration

Calibrating an RF vector network analyzer (VNA) requires three standard test loads: a short circuit, an open circuit, and a 50-ohm termination. This SOL (Short-Open-Load) calibration procedure characterizes the systematic errors of the VNA's test port — cable losses, connector reflections, and port mismatch — so they can be mathematically removed from subsequent measurements.

The three loads provide three known reference conditions: total reflection with zero phase shift (short), total reflection with 180-degree phase shift (open), and perfect absorption with no reflection (50-ohm load). From these three references, the VNA's error correction model can be fully determined.

What a VNA Measures

A two-port vector network analyzer can measure filter frequency response — the variation in transmission (S21) as a function of frequency. This is one of the most common VNA applications: characterizing bandpass filters, low-pass filters, and high-pass filters to verify their frequency response matches specifications.

A VNA can also measure input impedance, output impedance, and reflection coefficient — all of these are correct measurements for a VNA. Phase noise is measured by a phase noise analyzer, not a VNA. Pulse rise time is measured by an oscilloscope. Forward power is measured by a wattmeter.

Forward and Reflected Power

When a directional power meter reads 100 watts forward power and 25 watts reflected power, the power absorbed by the load is 75 watts. The absorbed power is the difference between forward and reflected power:

The reflected power is not added to the forward power (which would be incorrect), and the absorbed power is not a midpoint calculation. The simple difference gives absorbed power directly.

Measuring Q

The Q (quality factor) of a series-tuned circuit can be determined from the bandwidth of the circuit's frequency response. Q is defined as the resonant frequency divided by the 3 dB bandwidth: Q = f₀ / BW. By measuring the resonant frequency and the bandwidth between the two half-power (−3 dB) points, Q can be calculated directly.

The ratio of inductive to capacitive reactance at resonance is always 1:1 (they are equal at resonance), so that ratio does not determine Q. Frequency shift and resonant frequency alone are not sufficient — the bandwidth measurement is the key quantity.

Intermodulation Distortion Testing

The correct method for measuring intermodulation distortion (IMD) in an SSB transmitter is to modulate the transmitter using two audio frequency (AF) signals having non-harmonically related frequencies and observe the RF output with a spectrum analyzer. Two-tone testing uses audio tones (not RF signals at the input) to drive the transmitter's microphone input. The tones must be non-harmonically related (such as 700 Hz and 1900 Hz) so that their intermodulation products fall at unique, identifiable frequencies in the output spectrum.

Using harmonically related tones would cause IMD products to overlap with the tones' harmonics, making them impossible to distinguish. Using RF signals at the input (rather than AF tones) does not test the audio chain's contribution to IMD. A peak-reading wattmeter cannot resolve individual spectral products. Only a spectrum analyzer provides the frequency resolution needed to see individual IMD products.

E4B Practice Questions