Bias-T

The plunger and barrier gates of quantum dots have a DC voltage offset to maintain the desired operational regime. The gates are pulsed for the initialization, manipulation and readout of the qubit state. The DC voltage source and the AWG-generated pulses are combined by means of a bias-T.

../../_images/bias_T.png

Bias-T connecting the high frequency AWG and the low frequency DAC to the device.

The bias-T is a T-like component which acts as a high-pass filter for the AWG pulses and as a low-pass filter for the DC voltage. It consists of a resistor and a capacitor with values in the order of 1 MOhm and 100 nF giving an RC-time in the order of 0.1 s. The a cut-off frequency \(f_c = 1/2\pi R C\) is in the order of a few Hz.

he high-pass filter on the AWG signal results in amplitude decays for long pulses and accumulation of an offset when the average voltage of a sequence is not zero. This offset will grow with every repetition of the sequence until the offset is has the negative voltage of the average of the sequence.

../../_images/bias_T_block_pulse.png

Decay of the amplitude of a long block pulse due to the bias-T high pass filtering with RC-time = 0.1 s.

../../_images/bias_T_sequence.png

The deviation after 2 pulses of ~0.5 ms is only 1.6 mV. After 100 repetitions the deviation is > 50 mV.

DC-compensation

The average voltage of a sequence should be 0.0 V to avoid a growing voltage offset due to the bias-T high pass filtering. Pulse_lib will automatically add a DC-compensation pulse when the average of a sequence is not zero. This DC-compensation is enabled for all channels where the channel compensation limits are set.

Note: Contrary to all other settings, the compensation limits are set in AWG voltage, not the device voltage.

Example:

Enable DC-compensation for channels P1 and P2 with limits of -200 and +500 mV.

pl.add_channel_compensation_limit('P1', (-200, 500))
pl.add_channel_compensation_limit('P2', (-200, 500))
../../_images/DC_compensation_pulses.png

DC compensation with automatically added pulses of -200 mV at the end of the sequence.

Bias-T compensation

Sequences with long pulses or long sequences with the average voltage not equal to zero will be distorted by the bias-T when the duration exceeds a few percent of the RC-time. Pulse_lib will compensate for the bias-T high-pass filtering when the bias-T time compensation is configured. This bias-T correction will increase the sequence compilation time with a small percentage.

The bias-T compensation can correct pulses with a duration in the order of the RC-time. Pulses that are longer than a few times the RC-time will eventually hit the limits of the AWG output range, because the bias-T compensation increases the amplitude of the signal. A good correction of long pulses is only possible when the configured RC-time is accurate enough. An error of 2% in the configured RC-time gives an error of 10% in the amplitude at the end of a pulse with a duration of 5 times the RC-time.

Note: The time of the bias-T is specified in seconds!

Example:

Enable bias-T compensation for channels P1 and P2.

pulse.add_channel_bias_T_compensation('P1', 0.102)
pulse.add_channel_bias_T_compensation('P2', 0.106)
../../_images/long_pulses_with_compensation.png

Bias-T compensated pulses. The dashed lines show the signal after bias-T with the desired rectangular pulses.