Dynamic suppression of unwanted frequency components with an HF2LI

There are many experimental situations in which the component of interest in a signal is not the strongest one, but some other related component, for instance the side bands in amplitude or frequency modulated signals. In such a case, the presence of the carrier at the input of the lock-in amplifier may be a hindrance, especially when the interesting component is much smaller than the carrier. The large dynamic reserve of Zurich Instruments’ Lock-in Amplifiers makes it possible to measure with high accuracy even components that are orders of magnitude smaller than the strongest component, but there are situations in which a cancellation of the dominant may be desirable.

The HF2LI Lock-in Amplifier is particularly well equipped to perform such an operation. In this blog we will see how it can be set up with different option configurations.

 

Implementations

All the experiments below were performed on an Amplitude Modulated signal (100 mVpk, 20% modulation index, 10 kHz carrier frequency and 100 Hz modulation frequency) generated by an Agilent 33500B waveform generator. The signal was split in two and fed to the two positive inputs of the HF2LI.

Figure1_HF2LI-Agilent

Figure 1: Wiring for the experiment

Channel 2 is used to lock on the carrier frequency and to generate the cancelling signal. The output of channel 2 is connected to the negative input of channel 1. Figure 1 shows the connection schematics.

 

In other situations the carrier signal could be directly generated by the HF2LI and the side bands could be a consequence of external effects (e.g. Doppler measurements, frequency mixings, etc.). In that case, the carrier frequency is already referenced internally and there is no need to lock to an external signal.

 

In real-life situations, it is well possible that the carrier may change over time, requiring adjustments to the cancelling signal. For certain application it may be useful to write a control program, using the supplied libraries, to periodically perform the necessary adjustments.

After performing the optimisation, one should press the Autorange button for channel 1 to automatically select the new best range for the signal.

 

HF2LI with HF2LI-PLL Dual Phase-locked Loop option

The HF2LI-PLL Dual Phase-Locked Loop option is extremely useful for this kind of applications as it gives the user full control over the PLL that tracks the carrier frequency: from the PLL panel in ziControl, it is possible to select a centre frequency, as well as a range for the PLL to operate in. Carefully choosing the best values for these two parameters allows the PLL not to be influenced by the side bands even in more demanding situations when they may be very close in frequency to the carrier and/or have an amplitude that is a significant fraction of the carrier’s.

The user also has full control over the PLL dynamics, which can be very useful with trickier signals.

The Figure 2 shows the spectrum of the signal coming from the waveform generator without any carrier suppression, as indicated by the output of channel 2 being off.

Figure2_PLL-noCS

Figure 2: HF2LI-PLL option; spectrum of the signal without carrier suppression

Turning on the output of channel 2 provides the cancelling signal to input 1. As a starting point, one can use for output 2 the same amplitude of the carrier and a phase of 0º.

In order to optimise carrier suppression, one has to find the optimal phase as well as the best amplitude. The former can be controlled by changing the PLL “Set Point” field as shown in Figure 3:

Figure3_PLL-PLLsetup

Figure 3: HF2LI-PLL option; configuration of the PLL for phase control

The amplitude, instead, is controlled from the Lock-in tab:

Figure4_PLL-LIsetup

Figure 4: HF2LI-PLL option; amplitude setting and input range.

The Figure 5 shows that with a careful choice of parameters and iterating a few times between phase and amplitude adjustments, the carrier could be suppressed by about 70 dB.

Figure5_PLL-CS

Figure 5: HF2LI-PLL option; Spectrum of the signal after carrier suppression

 

HF2LI with HF2LI-MF Multi-frequency option

Carrier suppression using the HF2LI-MF Multi-frequency option works in a similar way, except that all the controls are located in the Lock-in MF tab.

Again, Figure 6 shows the signal as it comes from the waveform generator with no carrier suppression. In this case all demodulators are set to work with oscillator 2, set to follow the external reference on input 2.

Figure6_MF-noCS

Figure 6: HF2LI-MF option; spectrum of the signal without carrier suppression

The cancelling signal is generated by selecting one of the demodulators – I chose number 6 – in the output signal generation column for output 2. The phase of the signal is then controlled with the “phaseshift” field of that demodulator, and the amplitude in the Output 2 amplitudes column. Note the opposite sign of the phase shift with respect to the HF2LI-PLL version.

Figure7_MF-setup-CS

Figure 7: HF2LI-MF option; cancelling signal settings and spectrum of the signal after carrier suppression

The carrier suppression technique also in this case is very effective at removing the unwanted signal and the range for input 1 can be reduced to only account for the signal in the sidebands.

 

HF2LI with no extra option

It is also possible to perform a carrier cancellation using an HF2LI without any additional option, although with performance limitations due to the lack of control on the phase of the cancelling signal.

As in the previous two cases, Figure 8 shows the signal without any carrier suppression. The settings for channels 1 and 2, as well as the wiring, are identical to the ones for the HF2LI-PLL case. The cancelling signal controls are also similar, with the exception of the phase control.

Figure8_LI-noCS

Figure 8: HF2LI without options; spectrum of the signal without carrier suppression

Figure 9 shows the result of carrier suppression.

Figure9_LI-setup-CS

Figure 9: HF2LI without options; cancelling signal settings and spectrum of the signal after carrier suppression

Although it is possible to reduce the carrier amplitude, the lack of phase control makes the technique both less effective as well as more susceptible to external influences on the signal effective path lengths such as changes in the carrier frequency.

 

Conclusions

This blog showed three different ways to cancel an unwanted frequency component using the HF2LI Lock-in Amplifier.

Depending on the configuration, different levels of control are possible, and this translates to different levels of effectiveness.

In the ideal case used for the blog, the HF2LI-MF option produced a slightly better result than the HF2LI-PLL one, but in real cases, where the different frequency components may be closer in frequency or may vary significantly, the latter option offers a greater degree of flexibility and control.

The carrier suppression technique can also be performed using an HF2LI without options, but the lack of phase control leads to a lower effectiveness.