Mixer
RF and IQ modulator and demodulator models with interference and noise.
Description
The unit Mixer represents four complex mixers of the main frequency band as well as interference and noise. The block models four types of mixers: modulator, demodulator, IQ modulator and IQ demodulator. Signal distortion is IQ gain and phase mismatch where appropriate, and noise includes system noise and LO phase noise.
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The idealised block model Mixer assumes that the input and output ports are matched.
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The idealised block model Mixer is single band with an assumed carrier frequency value. Therefore, the block Mixer can only generate one sideband at the output.
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The mixer block mask icons are dynamic and indicate the current set of applied noise parameters. For more information, see. Mixer Block Icons.
Ports
Input
#
Input
—
time-dependent input signal
real scalar | real column | real column | complex scalar | complex column
Details
A time-dependent input signal given as a real scalar or column, complex scalar or column. The column represents consecutive time points.
| Data types |
|
| Complex numbers support |
Yes |
Output
#
Output
—
time-dependent output signal
complex scalar | complex column
Details
A time-dependent output signal returned as a complex scalar or column. The size of the output signal is equal to the size of the input signal.
| Data types |
|
| Complex numbers support |
Yes |
Parameters
Main
#
Type of mixer —
mixer type
mod | demod | iqmod | iqdemod
Details
Mixer Type. Defined as:
-
mod- modulator -
demod- demodulator -
iqmod- IQ modulator -
iqdemod- IQ demodulator
| Values |
|
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
#
Conversion gain for mixer (dB) —
conversion factor for the mixer
Real number
Details
The conversion gain for the mixer model, specified as a real number.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Sidebands of mixer —
mixer side strips
lower | upper
Details
Mixer Side Bands. Defined as:
-
lower. -
upper
Dependencies
To use this parameter, set the Mixer type parameters to mod.
| Values |
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| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
#
Rf carrier frequency (Hz) —
radio frequency carrier frequency
Real number
Details
The radio carrier frequency for the mixer model, specified as a real number.
Dependencies
To use this parameter, set the Mixer type parameters to mod, demod or iqdemod.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Local oscillator frequency (Hz) —
local oscillator frequency
Real number
Details
The frequency of the local oscillator for the mixer model, specified as a real number.
Dependencies
To use this parameter, set the Mixer type parameters to mod, demod, or iqdemod.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
Основные
#
LO phase offset (deg) —
LO phase offset
Real number
Details
LO phase offset specified as a real number.
Dependencies
To use this parameter, set the Mixer type parameters to mod or demod.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
IQ gain imbalance (dB) —
IQ gain imbalance
Real number
Details
The IQ gain imbalance specified as a non-negative real number.
Dependencies
To use this parameter, set the Mixer type parameters to iqmod or iqdemod.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
IQ phase imbalance (deg) —
IQ phase imbalance
Real number
Details
IQ phase imbalance given as a real number.
Dependencies
To use this parameter, set the Mixer type parameters to iqmod or iqdemod.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Third-order nonlinearity type —
third-order nonlinearity type
IIP3 | OIP3 | IP1dB | OP1dB | IPsat | OPsat
Details
The type of third-order nonlinearity in a cubic polynomial model. Defined as:
-
IIP3. -
`OIP3
-
`IP1dB
-
`OP1dB
-
`IPsat
-
`OPsat
| Values |
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| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
#
Input third-order intercept point —
third-order intercept input point
Real number
Details
A third-order intercept point specified as a positive real number.
Dependencies
To use this parameter, set the Third-order nonlinearity type parameter to IIP3.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Output third-order intercept point —
third-order intercept output point
Real number
Details
The output point of a third-order intercept specified as a positive real number.
Dependencies
To use this parameter, set the Third-order nonlinearity type parameter to OIP3.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Input 1 dB compression point —
input compression point 1 dB
Real number
Details
1 dB input compression point specified as a positive real number.
Dependencies
To use this parameter, set the Third-order nonlinearity type parameter to IP1dB.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Output 1 dB compression point —
output compression point 1 dB
Real number
Details
1 dB compression output point specified as a positive real number.
Dependencies
To use this parameter, set the Third-order nonlinearity type parameter to OP1dB.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Input saturation point —
input saturation point
Real number
Details
The input saturation point specified as a positive real number.
Dependencies
To use this parameter, set the Third-order nonlinearity type parameter to IPsat.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Output saturation point —
output saturation point
Real number
Details
The output saturation point specified as a positive real number.
Dependencies
To use this parameter, set the Third-order nonlinearity type parameter to OPsat.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
Основные
#
Options to mixer noise to system —
inclusion of mixer noise in the system
Logical
Details
Select this check box to add mixer noise to the input signal.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
#
Type of noise —
noise type
noise-temperature | NF | noise-factor
Details
Noise Type. Defined as:
-
noise-temperature- noise temperature -
NF- noise factor -
noise-factor- noise factor
Dependencies
To use this parameter, select the Options to mixer noise to system parameters checkbox.
| Values |
|
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
# Noise temperature (K) — mixer noise temperature
Details
The noise temperature for mixer noise modelling, specified as a non-negative real number.
Dependencies
To use this parameter, check the Options to mixer noise to system parameters and set the Type of noise parameter to noise-temperature.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Noise figure (dB) —
mixer noise figure
Real number
Details
The noise figure for modelling mixer noise, specified as a non-negative real number.
Dependencies
To use this parameter, check the Options to mixer noise to system parameter and set the Type of noise parameter to NF.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Noise factor to model mixer noise —
mixer noise figure
Real number
Details
The noise figure for modelling mixer noise, specified as a positive integer scalar, .
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Source of initial seed —
initial value source
auto | user
Details
The initial value source used to prepare the Gaussian random number noise generator. Defined as:
-
auto- the source for each mixer is generated using the random number generator. The instance reset method has no effect. -
user- if the Source of initial seed parameter is set toauto, the value specified in the Seed for random number generator property is used to initialise the random number generator, and the reset method resets the random number generator using the value of the Seed for random number generator property.
Dependencies
To use this parameter, check the Options to mixer noise to system or Add LO phase noise to LO signal parameters.
| Values |
|
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
#
Seed for random number generator —
source for the random number generator
Real number
Details
The initial value for the random number generator, specified as a non-negative integer, . Use this value to initialise the random number generator.
Dependencies
To use this parameter, check the Options to mixer noise to system or Add LO phase noise to LO signal parameters and set the Source of initial seed parameter to user.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Add LO phase noise to LO signal —
inclusion of LO phase noise to the LO signal
Logical
Details
Select this check box to add LO phase noise to the LO signal depending on the frequency.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
#
Phase noise level (dBc/Hz) —
phase noise level relative to the carrier
Scalar / array of real numbers
Details
The phase noise level relative to the carrier, specified as a negative real scalar or vector.
| The number of values listed in the Phase noise level relative to carrier parameter must be equal to the number of values in the Phase frequency offset parameter. |
Dependencies
To use this parameter, select the Add LO phase noise to LO signal parameters checkbox.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Frequency offset (Hz) —
phase frequency offset
Scalar / array of real numbers
Details
Frequency offset as a positive real scalar or vector of positive increasing real values.
| The number of values listed in the Phase frequency offset parameter must be equal to the number of values in the Phase noise level relative to carrier parameter. |
Dependencies
To use this parameter, check the Add LO phase noise to LO signal parameters.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Options to automatically determine number of frequency bins —
enabling automatic detection of the number of frequency bins
Logical
Details
Select this checkbox to automatically determine the number of frequency bins used in the two-way phase noise spectrum.
Dependencies
To use this parameter, select the Options to mixer noise to system and Add LO phase noise to LO signal parameters check boxes.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
#
Number of sample in time-domain signal —
number of samples in the signal in the time domain
Real number
Details
The number of samples in a time domain signal for blocks of sampling period or the number of frequency lines (bins) in the two-way frequency spectrum of a signal to achieve the required frequency resolution for a given frequency offset, specified as a valid non-negative integer, . The frequency resolution increases with increasing value of the number of samples of the signal.
| The value of this parameter should be equal to the power of two. |
Dependencies
To use this parameter, check the Options to mixer noise to system and Add LO phase noise to LO signal parameters.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Source of initial seed —
description missing
auto | user
Details
description missing
| Values |
|
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
#
Seed for random number generator —
description missing
Real number
Details
Description missing.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
Algorithms
Mixer block architectures and design equations
Here are the architectural models for the block Mixer. Here is the mixer and phase noise data for all cases.
Modulators and Demodulators
The modulator and demodulator architectures include system noise, phase noise, and nonlinear polynomials for carrier translation. A random number generator is used as input to generate phase noise.
The output of an ideal modulator and demodulator circuit with nonlinearities, , is given by this equation:
where
IQ modulator
The primary IQ modulator consists of two mixers, and . The mixers convert baseband signals into RF signals and are typically used in direct conversion architectures. The mixers and are responsible for introducing gain, gain imbalance, phase imbalance and nonlinearity into the IQ demodulator.
The output signal of the IQ modulator, , is defined as:
where
The linear gains of the modulators and are given in Eq:
where
IQ Demodulator
The architecture of the IQ demodulator is shown below. The in-phase, , and quadrature component, , of the modulated signal are the outputs of and , respectively. The mixers, and , are responsible for introducing gain, gain unbalance, phase unbalance and nonlinearity into the IQ demodulator.
The output of the IQ demodulator, , is as follows
where
The linear gains of the modulators and are given in this equation.
where
Mixer unit sidebands
Upper and lower sidebands
The expression for shows the formation of the upper and lower sidebands, and , and the effect of the difference between the input carrier and LO signal values on the sine function. Application of the trigonometric identity:
to the expression of the product of mixers, , gives
where the term associated with the higher output frequency, , is the upper sideband, and is the lower sideband. Set the Type of mixer parameters to mod.
For demodulators, only the lower sideband can be used as the output.
Selecting a mixer by type
When selecting a mixer type, this table shows the available sideband options according to the block parameters LO phase offset, IQ gain imbalance and IQ phase imbalance.
| Mixer type | Distortion | Noise |
|---|---|---|
Modulator |
LO phase offset and nonlinearities. |
LO phase offset, mixer and system noise. |
Demodulator |
||
IQ Modulator/Demodulator |
Gain imbalance, phase imbalance and nonlinearity. |
Mixer block icons
This table shows how the block icons will change depending on the values of the parameters Type of mixer, Options to mixer noise to system and Add LO phase noise to LO signal.
| Type of mixer | Options to mixer noise to system | Add LO phase noise to LO signal: off. | Add LO phase noise to LO signal: on. |
|---|---|---|---|
Modulator
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Demodulator
( |
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IQ Modulator
( |
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IQ-Demodulator
( |
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Literature
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Razavi, Behzad. "Basic Concepts in RF Microelectronics", 2nd edition, Prentice Hall, 2012.
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Kundert, Ken."Accurate and Rapid Measurement of IP2 and IP3," The Designer Guide Community, May 22, 2002.
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Kasdin, N.J.. "Discrete Simulation of Colored Noise and Stochastic Processes and 1/f α Power Law Noise Generation." Proceedings of the IEEE 83, no. 5 (May 1995): 802-27. https://doi.org/10.1109/5.381848.