How do I demodulate a signal at a higher harmonic with an external (PLL) reference?
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Moku:Lab's Lock-in Amplifier (LIA) uses a phase-locked loop (PLL) to capture the external reference signal and then generates a pair of sine waves at the same frequency to demodulate the input signal. The PLL does not have a built-in frequency multiplier. However, it may be possible to manually set the PLL frequency to capture the reference at a higher harmonic, which enables the higher harmonic demodulation. This method may (only) work at higher frequencies, and when the input signal is not a sine wave.
A perfect sine wave reference does not contain any higher harmonic components. A perfect square wave reference does not contain any even harmonic components. However, at higher frequencies (i.e. 10 MHz), distortions induced by the amplifier, nonlinear phase response, and other factors become more significant. The detected reference input will contain some higher components. Some analog frontend settings can significantly increase these effects. As most of these effects do not induce additional frequency invariants into the system, the measured result from the LIA will not be significantly degraded.
Here are the recommended steps to lock the LIA's reference at the second harmonic of a 10 MHz square input:
1) Connect the input at Moku:Lab's input 2. Launch the Spectrum Analyzer, enable input 2, and set the span to cover 10 MHz to about 30 MHz.
2) Adjust the front-end settings: coupling, impedance, and input range. Write down the settings that create the largest 2nd harmonic component. In the following figure, we compared the result from [50 Ω, 10 Vpp], and [1 MΩ , 1 Vpp] settings. The latter setting is desired for a higher 2nd harmonic component (+71.5 dBm above baseline).
3) Launch the LIA and set the instrument to external (PLL) mode. Set the frontend for input 2 as 1 MΩ, 0 dB (1 Vpp). Enable the probe point before and after the PLL.
4) Click or tap the PLL block, then manually enter 20 MHz as the frequency. Keep a close eye on the signal display while adjusting the tracking bandwidth. Choose a bandwidth where the phase relation between the reference and generated sine wave is most stable. Please note 1) You may need to tap/click reacquire every time you change the bandwidth. 2) The frequency measurement from the built-in probe point is based on windowed FFT. The accuracy varies with different time span settings. With some spans, the measured output frequency may not be exact at twice the input frequency.
5) Observe the signal for a few minutes and make sure the PLL can lock on the 2nd harmonic. If a stable lock can be established, the LIA will be able to demodulate the signal at this harmonic.
Final remark: It is crucial for LIA measurement that the PLL can accurately lock and track the input reference signal's frequency. Please pay extra attention to monitor the PLL and ensure a stable lock is established during the measurement.