Signal Generation and Output

Each Wave Output of the

The Output tab provides the electrical configuration of the Wave outputs and all configuration of the AWG and sine generator signals. It is available on all HDAWG instruments.

Features

• Sequencer start/stop control
• Dynamic layout for 1x8, 2x4, 4x2 channel grouping
• Sine generator configuration: frequency, harmonic, phase, amplitude
• AWG modulation control
• Output enable, range, amplification, and filter settings

Description

Table 1: App icon and short description

Control/Tool	Option/Range	Description
Output		Quick overview and access to all the settings and properties for signal generation and modulation.

The Output tab (see Figure 1) is divided into four sections: Oscillators, Sine Generators, Waveform Generators, and Wave outputs.

Figure 1: LabOne UI: Output tab

The purpose of the Output tab is to configure how the waveform signals previously prepared in the AWG Sequencer tab are routed to the Wave outputs of the instrument. The tabular layout of the tab provides a quick overview of the status of the different AWG cores on the instrument (see AWG Architecture and Execution Timing for an overview on the internal architecture and terminology), and enables quick access to all necessary settings to configure the modulation (i.e. multiplication) and addition of sinusoidal and AWG signals.

Conceptually, the tab is laid out as follows: The Wave Outputs section represents the physical outputs of the device in horizontal rows. The signal on a given Wave output can be a multiplication, or addition, or both, of AWG and sine signals, depending which modulation mode is used.. The Signal field contains a representation of the current signal generated on one output in the form of a simple formula (e.g., "Sine_1*AWG_1 + Sine_2").

The individual Sine and AWG signals are configured in the Sine Generators and Waveform Generators section. The horizontal rows in these sections represent the digital signals generated by the Sine Generators and Arbitrary Waveform Generator channels. The Output Amplitudes section represent the pair-wise matrix-like routing of these signal (rows) to the Wave outputs (columns).

The rows in the Waveform Generator and the Sine Generators section are graphically grouped in two, and each pair is associated with a pair of Wave outputs. This arrangement reflects the AWG Architecture and Execution Timing of the instrument, where one front end FPGA per pair of Wave outputs contains one dual-channel AWG core, and one pair of sine generators.

The different choices in the Modulation setting for each channel correspond to different settings of the Signal Routing and Modulation block (see AWG Architecture and Execution Timing). The block diagram in HDAWG Signal Routing and Modulation. and provide a mapping between Modulation setting and switch states. illustrates this block with its internal switches controlled with the Modulation setting. Table 2 and Table 3 map the Modulation settings to the states of the switches A through F in the block diagram. Note that the states of the switches B and C are only relevant when a signal from AWG output 1 is explicitly routed to Wave Output 2, or from AWG output 2 to Wave Output 1. This is the case e.g. when using sequencer instructions of the form playWave(1, 2, w), playWave(1, 2, w_a, 1, 2, w_b), playWave(1, w_a, 1, w_b). In the standard form of dual-channel waveform playback using playWave(w_a, w_b) on one core, this is not the case and only the switch states A, D, E, and F are relevant. Please refer to Multi-Channel Playback Tutorial for more details on the topic of AWG output assignment.

Figure 2: HDAWG Signal Routing and Modulation.

Table 2: Switch configuration for different Modulation settings on Wave Output 1

Modulation setting	Switch A state	Switch B state	Switch E state
Off	3	3	2
Sine 11	1	1	2
Sine 12	1	2	2
Sine 21	2	1	2
Sine 22	2	2	2
Advanced	3	3	1

(AWG Core 1). Switch B state is only relevant when using non-standard AWG output assignment (see main text).

Table 3: Switch configuration for different Modulation settings on Wave Output 2

Modulation setting	Switch C state	Switch D state	Switch F state
Off	3	3	2
Sine 11	1	1	2
Sine 12	1	2	2
Sine 21	2	1	2
Sine 22	2	2	2
Advanced	3	3	1

(AWG Core 1). Switch C state is only relevant when using non-standard AWG output assignment (see main text).

In addition to the modulation modes described above, there is a further mode called Mixer Calibration which is not covered by the tables and diagram above. Since this mode uses up to four signal added on one Wave output, it is clearer to document the generated output signal in terms of formulas. In order to describe the signals, we use the following nomenclature:

• Sine1: Signal of Sine Generator 1
• Sine2: Signal of Sine Generator 2
• AWG1: Signal of AWG Core 1, Output 1
• AWG2: Signal of AWG Core 1, Output 2
• Gain11: First AWG gain parameter on Wave 1 (device node AWGS/0/OUTPUTS/0/GAINS/0)
• Gain21: Second AWG gain parameter on Wave 1 (device node AWGS/0/OUTPUTS/0/GAINS/1)
• Gain12: First AWG gain parameter on Wave 2 (device node AWGS/0/OUTPUTS/1/GAINS/0)
• Gain22: Second AWG gain parameter on Wave 2 (device node AWGS/0/OUTPUTS/1/GAINS/1)

The figure below shows the location of the AWG gain parameters in the AWG Output tab.

Figure 3: HDAWG Location of the AWG Gain setting sin the LabOne UI in the nomenclature introduced in the main text.

By using an AWG sequence instruction of the form playWave(1, 2, w_I, 1, 2, w_Q);, where the waveforms w_I and w_Q are in-phase and quadrature components of a pulse, we route activate the routing of both AWG output signals to both Wave outputs. Using the modulation mode setting, we define the method with which they are modulated. The following table describes the signal generated on Wave 1 depending on the modulation setting of channel 1.

Table 4: Wave 1 signal depending on the chosen modulation mode.

Modulation mode channel 1	Wave 1 Signal
Off	Gain11*AWG1 + Gain21*AWG2
Sine11	Gain11*AWG1*Sine1 + Gain21*AWG2*Sine1
Sine12	Gain11*AWG1*Sine1 + Gain21*AWG2*Sine2
Sine21	Gain11*AWG1*Sine2 + Gain21*AWG2*Sine1
Sine22	Gain11*AWG1*Sine2 + Gain21*AWG2*Sine2
Mixer Calib	AWG1*(Sine1*Gain11 - Sine2*Gain21) + AWG2*(Sine1*Gain21 + Sine2*Gain11)

The following table describes the signal generated on Wave 2 depending on the modulation setting of channel 2.

Table 5: Wave 2 signal in different Modulation modes.

Modulation mode output 2	Wave 2 Signal
Off	Gain12*AWG1 + Gain22*AWG2
Sine11	Gain12*AWG1*Sine1 + Gain22*AWG2*Sine1
Sine12	Gain12*AWG1*Sine1 + Gain22*AWG2*Sine2
Sine21	Gain12*AWG1*Sine2 + Gain22*AWG2*Sine1
Sine22	Gain12*AWG1*Sine2 + Gain22*AWG2*Sine2
Mixer Calib	AWG1*(Sine1*Gain12 - Sine2*Gain22) + AWG2*(Sine1*Gain22 + Sine2*Gain12)

Analogous expressions hold for channel pairs 3&4, 5&6, 7&8 (AWG Cores 2, 3, 4).

We may write the modulation operations in matrix form:

\[\begin{equation} \begin{pmatrix} \mathrm{Wave1} \\\ \mathrm{Wave2} \end{pmatrix} = \begin{pmatrix} \mathrm{Gain11} & \mathrm{Gain21} \\\ \mathrm{Gain12} & \mathrm{Gain22} \end{pmatrix} \begin{pmatrix} \mathrm{Sine1} & \mathrm{Sine2} \\\ -\mathrm{Sine2} & \mathrm{Sine1} \end{pmatrix} \begin{pmatrix} \mathrm{AWG1} \\\ \mathrm{AWG2} \end{pmatrix} \end{equation}\]

Mixer Calibration

A perfect IQ mixer generates the following signal V_RF(t) at its RF port:

V_RF(t)= V_I(t)cos(ω_LOt) + V_Q(t)sin(ω_LOt)

where V_I(t) and V_Q(t) are input signals at the mixer I and Q ports, and ω_LO is the local oscillator frequency. A real mixer is characterized by a certain phase imbalance θ and amplitude imbalance α, so that it effectively performs the following operation:

V_RF(t)= V_I(t)cos(ω_LOt) + V_Q(t)sin(ω_LOt+θ)α

In order to generate a continuous signal at the lower sideband ω_LO-ω relative to the local oscillator frequency, and at the same time suppress the upper sideband ω_LO+ω, the following signals need to be applied to the mixer I and Q ports:

V_I^-(t) = cos(ωt)

V_Q^-(t) = sin(ωt-θ)/α

Conversely, in order to generate a signal at the upper sideband ω_LO+ω, the following signals need to be applied:

V_I⁺(t) = cos(ωt)

V_Q⁺(t) = -sin(ωt+θ)/α

In order to generate a phase-modulated pulse (e.g. a DRAG pulse) with these imbalance parameters θ and α at the upper sideband, proceed as follows: - Set the modulation mode of channels 1 and 2 to Mixer Calib. - Connect Sine Generators 1 and 2 both to the same oscillator (e.g. oscillator 1) - Set the phase of Sine Generator 1 to 90 degrees - Set the phase of Sine Generator 2 to 0 degrees - Determine a normalization parameter λ = 1/(1 + |tan(θ)| + |sec(θ)/α|) - Set Gain11 to λ - Set Gain21 to -λ×tan(θ) - Set Gain12 to 0 - Set Gain22 to λ×sec(θ)/α - Play AWG signals using an instruction of the form playWave(1, 2, w_I, 1, 2, w_Q);, where the waveforms w_I and w_Q are in-phase and quadrature components of the pulse

In this configuration, Sine Generator 1 will generate a signal cos(ωt) with the frequency ω of the oscillator. Sine Generator 2 will generate a signal sin(ωt). The Wave outputs will generate the following signals:

Wave 1 signal: λ×(w_I×(cos(ωt)×1 + sin(ωt)×tan(θ)) + w_Q×(-cos(ωt)×tan(θ) + sin(ωt)×1) )

Wave 2 signal: λ×(w_I×(cos(ωt)×0 - sin(ωt)×sec(θ)/α)) + w_Q×(cos(ωt)×sec(θ)/α) + sin(ωt)×0))

The normalization parameter λ<1 ensures that the sum remains smaller than 1 at all times. This prevents clipping caused by an overflow of the digital signal that enters the digital-to-analog converter.

We may write the operation of the output modulation stage in this configuration in matrix form:

\[\begin{equation} \begin{pmatrix} \mathrm{Wave1} \\\ \mathrm{Wave2} \end{pmatrix} = \begin{pmatrix} 1 & -\tan(\theta) \\\ 0 & \sec (\theta)/\alpha \end{pmatrix} \begin{pmatrix} \cos (\omega t) & \sin (\omega t) \\\ -\sin (\omega t) & \cos (\omega t) \end{pmatrix} \begin{pmatrix} \mathrm{w\_I} \newline \mathrm{w\_Q} \end{pmatrix} \end{equation}\]

In order to generate a signal at the lower sideband of the LO frequency, it is recommended to use the settings as above, however set the frequency of the AWG oscillator to the desired negative value.

Functional Elements

Table 6: Output tab

Control/Tool	Option/Range	Description
Frequency (Hz)	0 to 1.2 GHz	Frequency control for each oscillator.
Frequency (Hz)		Oscillator frequency when AWG Oscillator Control is enabled. In this mode, the frequencies cannot be changed from the user interface, but only through an AWG sequence program. When disabling AWG Oscillator Control, the frequencies are reset to the previous setting.
Oscillator Selection	1 to 16	Selection of the oscillator used for the generated sine signal.
Harmonics	1 to 1023	Multiplies the oscillator's reference frequency with the integer factor defined by this field.
Phase	-180 to +180 degree	Sets the phase of the sine signal.
Amplitude	0 to 5 V (depending on range)	Sets the amplitude of the sine signal.
Enable	ON / OFF	Enables the given sine signal (row) to the Wave output (column). The signal is added to other signals present on the given Wave output.
Channel Grouping		Sets the channel grouping mode of the device. Can only be changed when all AWG cores are stopped.
	MDS	Use the Wave outputs from MDS synchronized devices.
	4x2 or 2x2	Use the Wave outputs in groups of 2. One sequencer program controls 2 outputs. (use /dev..../awgs/0..4/)
	2x4 or 1x4	Use the Wave outputs in groups of 4. One sequencer program controls 4 outputs. (use /dev..../awgs/0/ and /dev..../awgs/2/)
	1x8	Use the Wave outputs in groups of 8. One sequencer program controls 8 outputs. Requires 8-channel instrument. (use /dev..../awgs/0/)
Oscillator Control		Sets the oscillator control mode of the device.
	UI/API	Oscillators are controlled by the UI/API.
	AWG	Oscillators are controlled by the AWG sequencer.
Start		Runs the AWG Sequencer. In MDS mode, use the start button on the sequencer tab to start all Sequencers in the correct order.
Hold		Keep the last sample (constant) on the output even after the waveform program finishes. It is recommended to use only AWG waveforms with lengths equal to a multiple of 16 together with this functionality. Waveforms with other lengths are automatically padded with zeros at the end by the AWG Compiler. The status of the hold node is checked only when the AWG is enabled. If hold is disabled after enabling the AWG or when the AWG is not running, AWG output values will still be held.
Modulation		Sets the modulation mode of the given AWG output. The notation Sine NM with N, M = 1, 2, ... signifies the following: the given AWG output is multiplied with the signal of Sine Generator N when routed to the first Wave output of the given AWG core, and with the signal of Sine Generator M when routed to the second Wave output of the given AWG core. In Advanced mode, 4 envelope signals are generated with the given AWG output using sample interleaving. Each envelope is multiplied with one sinusoid signal generated by the MF Modulation block represented in the MF Modulation tab. In Mixer Calibration mode, the AWG outputs are multiplied with the sum or difference of Sine Generators multiplied by gains specified so that the resulting output signal is ( AWG1*(Sine1*Gain1 - Sine2*Gain2) + AWG2*(Sine1*Gain2 + Sine2*Gain1) ).
Amplitude		Sets the amplitude scaling factor of the given AWG channel. The amplitude is dimensionless scaling factor applied to the digital signal.
Enable		Indicates the routing of the AWG signal (row) to the Wave output or to the digital mixer input (column).
Signal	string	Indicates which signals are combined to generate the output wave.
Offset (V)	-2.5 V to +2.5 V	Sets the analog offset voltage of the Wave output in amplified mode. The set value applies to a high-impedance load. For a 50 Ω load, the voltage at the load is half of the set value.
Delay		Delay the output of the signal in order to align waves.
Delay Status	red/green	Indicates the status of setting the delay. Red: Output is either turned off, or the delay setting is still in progress. Green: Delay has been set and output is ready.
Direct	ON / OFF	Enables the direct output mode in which the signal from the digital-to-analog converter is connected to the Wave connector without further amplification. This mode provides the highest bandwidth and lowest broadband noise. The range is fixed to 800 mV, and the signal contains spurs at the sampling frequency due to the absence of anti-alias filtering.
Range	200 mV to 5 V	Defines the maximum output voltage that is generated by the corresponding Wave output. This includes the potential multiple AWG and Sine Amplitudes and Offsets summed up. Select the smallest range possible to optimize signal quality.
Filter	ON / OFF	Enables the analog output filter.
On		Main switch for the Wave output corresponding to the LED indicator on the instrument front panel.