Update I/Q Modulation authored by Sander Snoo's avatar Sander Snoo
......@@ -11,8 +11,8 @@ The output of this mixer is:
$`y(t) = I(t) cos(\omega_c t) - Q(t) sin(\omega_c t)`$
IQ modulation can be used to create a single frequency output signal which is higher of lower in frequency
than the MW source. For this the IQ modulation signals should be sinusoids with a 90 degrees shift.
I/Q modulation can be used to create a single frequency output signal which is higher of lower in frequency
than the MW source. For this the I/Q modulation signals should be sinusoids with a 90 degrees shift.
$`I(t) = A(t) cos(\omega_m t + \phi(t))`$
......@@ -22,15 +22,15 @@ $`y(t) = A(t) [cos(\omega_m t + \phi(t)) cos(\omega_c t) - sin(\omega_m t + \phi
$`y(t) = A(t) cos((\omega_c + \omega_m) t + \phi(t))`$
IQ modulation allows frequency multiplexing, because it is a linear operation.
I/Q modulation allows frequency multiplexing, because it is a linear operation.
The I and Q components can contain multiple frequencies which will all be shifted with $`f_c`$.
IQ modulation can also be used for fast chirps (frequency sweeps), because phase
I/Q modulation can also be used for fast chirps (frequency sweeps), because phase
and frequency of the I and Q components can be swiftly changed by the AWG.
# I/Q modulation in pulse-lib
Users of pulse-lib don't have to care about the calculation of I and Q outputs.
They can specify the desired MW pulses after IQ modulation and pulse-lib calculates the I and Q output signals for the AWG.
They can specify the desired MW pulses after I/Q modulation and pulse-lib calculates the I and Q output signals for the AWG.
The user has to specify the I and Q output channels of the AWG as an I/Q pair and pass the frequency of the vector signal generator, the LO frequency.
For coherent qubit control every qubit needs a channel with the resonant frequency of the qubit.
......@@ -62,7 +62,7 @@ and the mirror side-band.
![real_modulation](uploads/704a0eac1aa034f74edb2c69dba114f5/real_modulation.png){width=900 height=216}
*IQ modulation in practice containing the carrier frequency and a mirrored side-band.*
*I/Q modulation in practice containing the carrier frequency and a mirrored side-band.*
## Offset error
......@@ -102,7 +102,7 @@ $`y(t) = cos(\frac{a}{2}) cos((\omega_c + \omega_m) t) - sin(\frac{a}{2}) sin((\
# I/Q corrections in pulse-lib
A vector signal generator will have options to correct the offset, phase and gain error of the IQ input, but only with a frequency independent correction.
A vector signal generator will have options to correct the offset, phase and gain error of the I/Q input, but only with a frequency independent correction.
Pulse-lib can also correct for these errors, where gain and phase corrections are frequency dependent.
Example:
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