Automating IQ mixer calibration on the HDIQ

As a crucial step in the bring-up of superconducting experiments, IQ mixer calibration normally requires multiple instruments from different parties and manual cabling work. This blog post describes how to use the Zurich Instruments HDIQ, HDAWG and UHFQA (or other UHF instruments) to automate IQ mixer calibration and:

  • Simplify the calibration routine, thus shortening the system characterization time.
  • Lower the probability of potential failure due to cable reconnection, thus increasing calibration reliability.

Measurement Setup

To have a clear view of the measurement method, only 1 IQ mixer is introduced. Automation of multi-mixer calibration and switch from mixer calibration to qubit experiment will be introduced at the end of the post. The type of mixer calibration discussed here is done with continuous-wave signals.

The measurement diagram is shown in Fig. 1, and all signal sources must use the same reference clock, e.g., the one taken from the UHFQA. The functionalities of the instruments and the RF components in the mixer calibration experiment are as follows:

  • HDIQ as IQ mixers for frequency up-conversion. The RF signal after IQ mixing will be sent out to the “Calib.” port for mixer calibration and to the “Exp.” port for the qubit experiment controlled by a digital input signal or a host computer via Ethernet.
  • HDAWG as an IF source generates the I and Q signals with compensation terms.
  • UHFQA as a spectrum analyzer that takes an input IF signal after frequency down-conversion. Only Signal Input 1 is used for mixer calibration.
  • LO1 as a microwave source for qubit control.
  • LO2 as a microwave source for frequency down-conversion at the mixer calibration stage and for qubit readout at the qubit experiment stage.
  • Coaxial IQ mixer as a tool for frequency down-conversion.

 

Figure 1. Mixer calibration measurement diagram.

 

It is worth mentioning that the measurement setup can be further simplified by using the SHFQA instead of LO2, the UHFQA, and the IQ mixer for frequency down-conversion.

Measurement Method

Once the qubit frequency measured by the same setup is known, the signal frequencies fLO1 of LO1 and fIF of the HDAWG are fixed. To calibrate the IQ mixer, the frequency of LO2 must be different from that of LO1, and the frequency difference should not be equal to a multiple of fIF. In the measurement, we assume the qubit frequency is 5.610 GHz, and that fLO1 = 5.5 GHz, fIF = 110 MHz, and fLO1 – fLO2 = 290 MHz. Therefore, LO leakage can be minimized by searching a global minimum of the signal amplitude at 290 MHz after frequency down-conversion. As the qubit frequency is on the right sideband, the signal at fLO1 – fIF – fLO2 = 180 MHz has to be minimized. If the qubit frequency is 5.390 GHz, then the signal at 400 MHz has to be suppressed.

A number of preparation steps must be taken before the measurement:

  • Power on all required instruments and connect the HDIQ, the HDAWG, and the UHFQA to a host computer. For the HDAWG and the UHFQA, please use the latest release of LabOne and its APIs. For the HDIQ, it will be possible to download the zhinst-hdiq Python package from https://github.com/zhinst/zhinst-hdiq from March 2021.
  • Set the operating mode of the HDIQ to “calibration” by following the example in the readme.md file.
  • Set the LO1 frequency and the HDAWG output modulation frequency according to the qubit frequency, in this case, fLO1 = 5.5 GHz, fIF = 110 MHz.
  • Set the LO2 frequency to fLO2 = fLO1 – 290 MHz.
  • Set the output power of LO1 to +5 dBm, and choose a suitable power for LO2.
  • Ensure that LO1, LO2, HDAWG, and UHFQA use the same reference clock.
  • Verify the correct connection of all instruments as shown in Figure 1.

Figure 2 shows the HDAWG “Output” tab, the “Scope” tab of the UHFQA, and the FFT signal after frequency down-conversion before mixer calibration. The signal at 290 MHz is due to LO leakage, whereas the signals at 180 MHz and 400 MHz are the left and right sideband, respectively. In this measurement, Wave Output 1 and 2 of the HDAWG are used.

 

Figure 2. LabOne GUI screenshot before mixer calibration.

 

LO Leakage Minimization

LO leakage is caused by the finite DC offset of the IQ mixer diode, therefore it can be corrected by adding an additional offset on the I and Q signals. The continuous IF signal is produced by the sine generators of the HDAWG as shown in Figure 2. By manually changing the I and Q offset in HDAWG Output → Waveform Generators → Offset (V), one can see the amplitude change of LO leakage at 290 MHz. With our Python code, the amplitudes of the I and Q offsets are swept in a nested loop, the signal amplitude is recorded with the UHFQA, and the new sweep center optimized from the previous measurement is used for the following loop with a smaller sweep range. Each data point is averaged by 20 times. The program plots a 2D image with the final sweep parameter as shown in Figure 3a. The amplitude of LO leakage drops from 0.02 V to 0.02 mV, and the suppression according to the desired right sideband signal is < -70 dBc.

 

Figure 3. LO Leakage and image sideband calibration result.

 

Sideband Suppression

Image sideband is caused by the imperfect phase difference and amplitude ratio of the IQ mixer and the cables used for connecting I and Q signals to the mixer, so it can be corrected by compensating the phase difference and the amplitude ratio of the I and Q input signals. As shown in Figure 2, by manually changing the phase of the Q signal and keeping the phase of the I signal to 0, and changing the amplitude ratio of the I and Q signals, one can observe the amplitude change of the left and right sidebands. With a similar optimization method, the global minimum of the left sideband can be found, as shown in Figure 3b. The image sideband suppression, in this case, is about -70 dBc. Moreover, the SFDR also is improved after the calibration (see Figure 4). The entire mixer calibration procedure discussed in this example takes about 3 minutes.

 

Figure 4. LabOne GUI screenshot after mixer calibration.

 

Switching From Mixer Calibration To Qubit Experiment
Because the HDIQ has separated ports for mixer calibration and for the qubit experiment, there is no need to change the cables on the HDAWG and the HDIQ. The only manual cabling work that is required is the connection of the RF signal in the readout line back to the UHFQA. In practice, an RF switch can be used to switch between mixer calibration and qubit readout, then completely removing all manual cabling work.

Multi IQ Mixer Calibration Automation

Multi IQ mixer in the same HDIQ or in multiple HDIQ instruments can be calibrated automatically in the same way as the one described above. The procedure can be fully automated without cable reconnection by using one or a few multi-port power combiners to combine all RF signals from the HDIQs to the UHFQA. This enables sequential mixer calibration, along with an RF switch that can be controlled to switch between mixer calibration and qubit readout.

Conclusion

By using the Python API and the HDIQ, the HDAWG, the UHFQA, LOs and an IQ mixer for frequency down-conversion, IQ mixer calibration can be fully automated with high suppression of LO leakage and image sideband. Since LO leakage optimization is a two-dimensional convex problem, the Nelder-Mead method is best suited for this task. For sideband calibration, Machine Learning could be used to speed up the optimization procedure. The code used to write this blog post can be provided upon request by sending an email to [email protected] or to [email protected]. More technical details can also be found in our application note “Frequency Up-Conversion for Arbitrary Waveform Generators”.

Leave a Reply