Signal sources
A DDS with a 100 MHz clock adjusts the frequency in steps of 0.023 Hz, but at 45 MHz its image is almost at the same level as the signal. That is why nobody uses it beyond 40% of its clock.
01Half of every measurement
To measure the response of an amplifier, a filter or a receiver, it must be excited with a known signal. The signal source is the other half of the measurement bench, and its imperfections —distortion, frequency error, phase noise, amplitude that changes with frequency— add to those of the circuit under test. Knowing how signals are generated makes it possible to tell when the generator limits the measurement.
02Analog function generators
The classic function generator starts from a triangle wave: an integrator charges a capacitor with a constant current and a comparator with hysteresis reverses the direction on reaching each threshold. The comparator output is the square wave, and the sine wave is obtained by rounding the triangle with a diode network that approximates the curvature piecewise, with a typical distortion of 0.5 to 1%. The frequency is changed with the charging current, which makes it possible to sweep it with a control voltage.
Low-distortion sine oscillators, such as the Wien bridge with amplitude control, are covered in the technician program, in oscillators.
03Direct digital synthesis
Almost all current generators use direct digital synthesis (DDS). An \( N \)-bit register, the phase accumulator, adds a number \( M \), the tuning word, on every clock cycle. Its value sweeps the phase from 0 to \( 2\pi \) and overflows to start over. The upper bits of the accumulator index a table with the sine values, and a DAC converts them into voltage:
The DAC output is a staircase: each sample is held for one clock period. This has two effects. The amplitude falls with frequency according to \( \sin(\pi f/f_{clk}) / (\pi f/f_{clk}) \), and images of the spectrum appear at \( f_{clk} \pm f_{out} \), \( 2 f_{clk} \pm f_{out} \)… A reconstruction filter removes them, which is why a DDS is used up to about 40% of its clock frequency: higher up, the image is too close to be filtered.
100 MHz clock, 32-bit phase accumulator and 14-bit DAC. Top, the samples coming out of the DAC (staircase) over the ideal sine wave, for two periods; bottom, the spectrum before the filter, with the fundamental and the first two images.
04Arbitrary, pulse and RF generators
| Generator | How it works | Key specification |
|---|---|---|
| Arbitrary waveform (AWG) | A memory with samples of any shape, read at a fixed rate | Sampling rate, memory length and DAC bits |
| Pulse | Pulses with adjustable width, period, delay and edges | Rise time, jitter |
| RF | A voltage-controlled oscillator locked with a PLL to a reference | Phase noise, calibrated output power, modulations |
The phase noise of an RF generator is the noise power at a given offset from the carrier, in dBc/Hz: for example, −110 dBc/Hz at 10 kHz. It limits the measurement of receivers and oscillators, because the generator’s noise is mixed up with that of the circuit.
05The output impedance
Almost all generators have 50 Ω of output impedance and display the amplitude assuming a 50 Ω load. If the load is high, such as the input of an oscilloscope or of an operational amplifier, the actual voltage is double the indicated one: the divider between the internal 50 Ω and the load no longer divides by two. Generators allow the load to be configured so that the indication matches. With intermediate loads the divider has to be calculated.
06In the laboratory
Program 1 V peak-to-peak on a generator and measure it with the oscilloscope at high impedance and with a 50 Ω termination. Explain the difference.
With a spectrum analyzer, observe the output of an unfiltered DDS module at several frequencies and measure the level of the first image. Compare it with the lab.
With a spectrum analyzer, measure the harmonic distortion of the sine wave of an analog function generator and of a DDS one.
07Common mistakes
- Forgetting the 50 Ω load. With an oscilloscope at high impedance, double the programmed value is measured.
- Using a DDS near half of its clock. The image is almost at the same level as the signal.
- Blaming the circuit for the generator’s distortion. The generator must be measured alone first.
- Trusting the frequency without checking the reference. The accuracy is that of the crystal, and an external 10 MHz clock improves the whole bench.
08Self-assessment
What tuning word gives 1 MHz in a 32-bit DDS with a 100 MHz clock?
\( M = 10^6 \cdot 2^{32} / 10^8 \approx 42\,949\,673 \).
How much does the amplitude of a DDS fall at a quarter of its clock frequency?
\( \sin(\pi/4)/(\pi/4) = 0.90 \): 0.91 dB.
A generator indicates 2 V into a 50 Ω load. What voltage does it give into a 1 MΩ load?
4 V.
Where does the first image of a 30 MHz output appear with a 100 MHz clock?
At 70 MHz.
09Further reading
- Analog Devices. A Technical Tutorial on Digital Signal Synthesis. Analog Devices, 1999. The reference tutorial on DDS: phase accumulator, truncation, spurs and images.
- Albert D. Helfrick and William D. Cooper. Modern Electronic Instrumentation and Measurement Techniques (Spanish edition: “Instrumentación electrónica moderna y técnicas de medición”). Prentice Hall, 1990. Signal and function generators, with their circuits.
- Ulrich L. Rohde and Enrico Rubiola. Microwave and Wireless Synthesizers: Theory and Design. 2nd ed., Wiley, 2021. Frequency synthesis with PLL and DDS, and phase noise in depth.