## Optimize Your Frequency Sweep for Static Impedance Measurement

Very often people want to measure very large static impedance (e.g. small capacitance, large resistance) over a wide frequency range. In the very low frequency region, one may notice that measured curve is not smooth but rather “jiggly”, just like the frequency response of a 100 pF capacitor measurement shown below. The values measured below 1 kHz are even very off from 100 pF.

This low frequency phenomenon occurs very often with capacitance measurement due to the fact that the amount of current flowing through a capacitor decreases as the measurement frequency goes down. At 1 Hz, we are actually trying to measure 1.59 GΩ of impedance with the 100 pF capacitor. Moreover, in this low frequency region, you might be measuring a signal current that is close to the 1/f noise. And depending on the type of sample being characterized, it is not always possible to increase the source voltage like for μElectrode or nanowire measurements. The transimpedance gain cannot be set too high in the high frequency region. Otherwise, you risk saturating at high frequencies during the frequency sweep or running into the gain-bandwidth product limitation of the amplifier.

### The 3A Principle

The real question is then: *Can we improve the frequency sweep measurement using the Sweeper? *Luckily, the short answer is a resounding *YES!* ziControl Sweeper provides the HF2 users a lot of flexibility to optimize the sweep settings under extreme conditions. Here are some useful tips when sweeping large impedance over a wide frequency range. The key is to think about the three A’s: **A**uto-range, **A**uto-bandwidth and **A**veraging.

### Auto-range

This little button can be a useful tool to help you optimize the frequency sweep operation. Once you have defined your lower and upper frequencies, first check the optimal input range by setting manually to lowest and then to the highest frequency. The input range for both frequencies can be found by pressing on the Auto-Range button as shown below. If the input is saturated, press on ‘A’ once to adjust the input range value. Note that you should keep the maximum range value for the frequency sweep which occurs usually at the highest frequency.

As an example, the auto-range values at different frequencies for a 100 pF capacitor are given in the table below.

One can see that the auto-range value is proportional to frequency (i.e. the input signal gets bigger as frequency goes up.) Obviously, one has to keep the largest range value over the whole 1 MHz frequency sweep range in order not to saturate the input channel. But this means also that the range value at 1 Hz will not be optimal: with 140 μA_{pk} setting, the measurement SNR at 1 Hz will be about 10 times or 20 dB worse than what it could have been with the 16 μA_{pk }setting.

One solution in this case is to split up the frequency sweep into two zones: 1 Hz to 1 kHz and 1 kHz to 1 MHz. With the split, the measurement at 1 Hz can retain its optimal auto-range value.

Hint: You will also be able to apply more gain at HF2TA when the signal is very weak since higher HF2TA gain can be set for lower frequencies.

### Auto-bandwidth

By default, the ‘Auto BW’ button is turned on in the Sweeper. But that is not the whole story. Auto BW works by assigning internally a filter bandwidth for each frequency point measured (note that the filter bandwidth is related to an integration time constant TC_{eff}). Furthermore, one can set the number of TC_{eff }to settle before a measurement point is taken. This is shown below and the default settling time is 3 TC_{eff}. By playing with this parameter, one will not only be able to improve 1/f noise filtering but also to reduce the overall sweep time.

Hint: This is a case where splitting up a sweep into different frequency regions can help to improve the sweep time. One may not want to have high TC_{eff} at higher frequencies where 1/f noise is negligible. Having only one sweep range will force all frequency points to wait for the same number of TC_{eff}.

### Averaging

This is often an overlooked Sweeper feature where it can really help to smooth out the frequency response curve. As it is shown below, one can have up to 256 points averaged for each measured frequency point. This flexibility can help to filter out noise in addition to the settling time adjustment described earlier. Again, splitting up frequency sweep regions can save time when more averaging is required at lower frequencies.

### Case Study

Now it’s time to put into practice the three A’s. The 4-Terminal setup is shown in the diagram below.

Hint: Using HF2CA buffer will give you better accuracy at low frequencies due to its higher input impedance. If voltage measurement port impedance is too low, then you may be measuring the input impedance of the port instead of your sample. Remember that we are measuring over 1 GΩ at 1 Hz in this example.

Below are the split sweep results of 100 pF capacitor divided into two sweep regions: 1 Hz to 1 kHz and 1 kHz to 1 MHz.

The swept parameters of the frequency sweeps are summarized in the table below.

One can see clearly that we have now a much less jiggly frequency response at low frequencies than the initial graph. As it turned out, Auto BW was not sufficient in noise filtering for measuring 100 pF at 1 Hz. I had to force a manual filter setting of 50 mHz by turning off Auto BW. But this was not so bad in terms of measurement time since I only swept 10 points from 1 Hz to 1 kHz at this bandwidth. The rest of the sweep of 30 points from 1 kHz to 1 MHz was done with Auto BW which went very fast. As a matter of fact, the 10 points took about 10 minutes while the rest of the 30 points took less than 1 minute. Here is a summary of observations:

- No big source amplitude required – only 100 mVpk
- By splitting up the frequency sweep, a much smaller range with a much larger HF2TA gain was possible which also helped to achieve better SNR
- The overall sweep time was dominated by lower frequency sweeps
- One may need to manually force the filter bandwidth in very high impedance cases

In any case, the divide-and-conquer philosophy for frequency sweeping could be a good approach for the majority of high impedance measurement cases. It saves time and helps to obtain more accurate response. Explore the Sweeper and ziControl settings described in this blog according to The 3A Principle should also help to improve static impedance measurement.