Mixer

Model RF and IQ modulator and RF and IQ demodulator with impairments and noise

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Libraries:
RF Blockset / Idealized Baseband

Description

The Mixer block models four complex baseband mixers and with impairments and noise. The four mixer types that the block models are Modulator, Demodulator, IQ Modulator, and IQ Demodulator. Impairments include IQ gain and phase mismatch where appropriate, while noise includes both system and LO phase noise.

Note

• Idealized Baseband library blocks assume input and output ports are matched. For more information on port signal power, see Power Ports and Signal Power Measurement in RF Blockset.

• Idealized Baseband library blocks are single carrier with assumed carrier frequency value. Therefore the Ideal Baseband Mixer block can produce only a single sideband output.

• Mixer block mask icons are dynamic and indicate the current set of applied noise parameters. For more information, see Mixer Block Icons.

Examples

Modulate Quadrature Baseband Signals Using IQ Modulators

Modulate quadrature baseband signals using two different RF Blockset™ blocks. You can use either an idealized baseband Mixer block or a circuit envelope IQ Modulator block in your model to modulate quadrature baseband signals to the RF level. Observe the impairments in the modulated output signal due to gain imbalance, third-order intercepts (OIP3) and system noise in the complex output power density and output power spectrum analyzers.

Open Script

Ports

Input

Port_1 — Time-dependent input signal

real scalar | real column | complex scalar | complex column

Time-dependent input signal, specified as a real scalar, real column, complex scalar, or complex column. A column represents consecutive time points.

Data Types: double | single

Output

Port_1 — Time-dependent output signal

complex scalar | complex column

Time-dependent output signal , returned as a complex scalar or complex column. The size of the output time dependent signal is equal in size to the input time dependent signal.

Data Types: double | single

Parameters

Main Tab

Mixer type — Type of mixer

Modulator (default) | Demodulator | IQ Modulator | IQ Demodulator

Mixers available in the Mixer block, specified as one of the following:

• Modulator

• Demodulator

• IQ Modulator

• IQ Demodulator

For more information, see Mixer Architectures and Design Equations.

Mixer sideband — Sidebands of mixer

Upper (default) | Lower

Sidebands of the mixer, specified as one of the one of the following:

• Lower

• Upper

For more information, see Mixer Sidebands.

Dependencies

To enable this parameter, set Mixer type to Modulator.

Input carrier frequency greater than LO frequency — Specify input carrier frequency as greater than LO frequency

on (default) | off

Specify whether the mixer baseband input carrier frequency is greater than the mixer LO frequency, specified as a logical.

Dependencies

To enable this parameter, set Mixer type to Modulator and Mixer sideband to Loweror Mixer type to Demodulator.

Conversion gain (dB) — Conversion gain for mixer

0 (default) | real number

Conversion gain for the mixer model, specified as a real number in dB.

Simulate using — Specify type of simulation to run

Interpreted execution (default) | Code generation

Type of simulation to run, specified as one of the following:

• Code generation — Simulate model using generated C code. The first time you run a simulation, Simulink^® generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change. This option requires additional startup time, but the speed of the subsequent simulations is faster than Interpreted execution.

• Interpreted execution — Simulate model using the MATLAB^® interpreter. This option shortens startup time speed, but the speed of the subsequent simulations is slower than Code generation. In this mode, you can debug the source code of the block.

Impairments Tab

LO phase offset (deg) — LO phase offset

0 (default) | real number

LO phase offset, specified as a real number in degrees.

Dependencies

To enable this parameter, set Mixer type to Modulator or Demodulator.

I/Q gain imbalance (dB) — IQ gain imbalance

0 (default) | nonnegative real numbers

IQ gain imbalance, specified as a nonnegative real numbers in decibels.

Dependencies

To enable this parameter, set Mixer type to IQ Modulator or IQ Demodulator.

I/Q phase imbalance (deg) — IQ phase imbalance

0 (default) | real numbers

IQ phase imbalance, specified as a real number in degrees.

Dependencies

To enable this parameter, set Mixer type to IQ Modulator or IQ Demodulator.

Type of Non-Linearity — Third-order nonlinearity type

IIP3 (default) | OIP3 | IP1dB | OP1dB | IPsat | OPsat

Type of third-order nonlinearity type in the cubic polynomial model, specified as IIP3, OIP3, IP1dB, OP1dB, IPsat, or OPsat.

For more information, see Nonlinearities in Idealized Baseband Mixer Block.

IIP3 (dBm) — Input third-order intercept point

Inf (default) | real positive number

Input third-order intercept point, specified as a real positive number in dBm.

Dependencies

To enable this parameter, set Type of Non-Linearity to IIP3.

OIP3 (dBm) — Output third-order intercept point

Inf (default) | real positive number

Output third-order intercept point, specified as a real positive number in dBm.

Dependencies

To enable this parameter, set Type of Non-Linearity to OIP3.

IP1dB (dBm) — Input 1 dB compression point

Inf (default) | real positive number

Input 1 dB compression point, specified as a real positive number in dBm.

Dependencies

To enable this parameter, set Type of Non-Linearity to IP1dB.

OP1dB (dBm) — Output 1 dB compression point

Inf (default) | real positive number

Output 1 dB compression point, specified as a real positive number in dBm.

Dependencies

To enable this parameter, set Type of Non-Linearity to OP1dB.

IPsat (dBm) — Input saturation point

Inf (default) | real positive number

Input saturation point, specified as a real positive number in dBm.

Dependencies

To enable this parameter, set Type of Non-Linearity to IPsat.

OPsat (dBm) — Output saturation point

Inf (default) | real positive number

Output saturation point, specified as a positive real number in dBm.

Dependencies

To enable this parameter, set Type of Non-Linearity to OPsat.

Plot power characteristics — Plot power characteristics

button

This button plots the power characteristics based on the value you specify in the Conversion gain (dB) parameter in the Main tab and the Type of Non-Linearity in the Impairments tab. When plotting power characteristics, the block ignores all other impairment values.

For more information, see Plot Power Characteristics.

Noise Tab

Include mixer noise — Add mixer noise to system

off (default) | on

Select this parameter to add mixer noise to the input signal. Once you select this parameter, the parameters associated with Include mixer noise are displayed and the mixer components in the block icon are shaded gray.

For more information, see Mixer (System) Noise Simulations.

Mixer noise type — Noise representation

Noise temperature (default) | Noise figure | Noise factor

Type of noise, specified as a Noise temperature, Noise figure, or Noise factor.

For more information, see Mixer (System) Noise Simulations.

Dependencies

To enable this parameter, select Include mixer noise.

Noise temperature (K) — Noise temperature to model mixer noise

290 (default) | nonnegative real number

Noise temperature to model the mixer noise, specified as a nonnegative real number in kelvin.

Dependencies

To enable this parameter, select Include mixer noise and set Mixer noise type to Noise temperature.

Noise figure (dB) — Noise figure to model mixer noise

10 * log10( 2 ) (default) | nonnegative real number

Noise figure to model the mixer noise, specified as a nonnegative real number in decibels.

Dependencies

To enable this parameter, select Include mixer noise and set Mixer noise type to Noise figure.

Noise factor — Noise factor to model mixer noise

2 (default) | positive integer scalar greater than or equal to 1

Noise factor to model mixer noise, specified as a positive integer scalar greater than or equal to 1

Dependencies

To enable this parameter, select Include mixer noise and set Mixer noise type to Noise factor.

Seed source, mixer noise — Source of initial seed

Auto (default) | User specified

Source of initial seed used to prepare the Gaussian random number noise generator, specified as one of the following:

• Auto — When you set Seed source, mixer noise to Auto, seeds for each mixer instance are generated using a random number generator. The reset method of the instance has no effect.

• User specified — When you set Seed source, mixer noise to User specified, the value provided in the Seed for mixer noise is used to initialize the random number generator and the reset method resets the random number generator using the Seed for mixer noise property value.

Dependencies

To enable this parameter, select Include mixer noise.

Seed for mixer noise — Seed for random number generator

67987 (default) | nonnegative integer less than 2³²

Seed for the random number generator, specified as a nonnegative integer less than 2³². Use this value to initialize the random number generator.

Dependencies

To enable this parameter, select Include mixer noise and set the Seed source, mixer noise parameter to User specified.

Include phase noise — Add LO phase noise to LO signal

off (default) | on

Select this parameter to add frequency-depended LO phase noise to the LO signal. Once you select this parameter, the parameters associated with the Include phase noise are displayed and the LO source inside the block icon is shaded gray.

For more information, see Phase Noise in Mixer Block.

Phase noise level (dBc/Hz) — Phase noise level relative to carrier

[-145 -150] (default) | negative real scalar | negative real vector

Phase noise level relative to carrier, specified as negative real scalar or vector in dBc/Hz.

Note

The number of terms listed in the Phase noise level (dBc/Hz) parameter must equal the number of terms in the Frequency offset (Hz) field.

Dependencies

To enable this parameter, select the Include phase noise parameter.

Data Types: double

Frequency offset (Hz) — Phase frequency offset

[1000 50000] (default) | positive real scalar | vector of positive increasing real values

Specify the frequency offset as a positive real scalar or vector of positive increasing real values of type double in Hz.

Note

The number of terms listed in the Frequency offset (Hz) must equal the number of terms in the Phase noise level (dBc/Hz) field.

Dependencies

To enable this parameter, select the Include phase noise parameter.

Automatic frequency resolution — Automatically determine number of frequency bins

on (default) | off

Select this parameter to automatically determine number of frequency bins used in a two-sided phase noise spectrum. You can also set the number of frequency bins using the Number of signal samples and Sample rate (Hz) parameters when you set the Automatic frequency resolution parameter is set to off.

Dependencies

To enable this parameter, click Include phase noise.

Number of signal samples — Number of samples in time-domain signal

0 (default) | real nonnegative integer less than or equaled to 65536

Number of samples in the time-domain signal for the blocks sample time or the number of frequency lines (bins) in the signals two-sided frequency spectrum to achieve the required frequency resolution for a specified Frequency offset, specified as a real nonnegative integer less than or equaled to 65536. Frequency resolution increases as the value of number of signal samples increases.

Note

The value of this parameter must be set to a power of two.

Dependencies

To enable this parameter, select the Include phase noise parameter and deselect Automatic frequency resolution.

Seed source, phase noise — Source of initial seed

Auto (default) | User specified

Source of initial seed used to prepare the Gaussian random number LO phase noise generator, specified as one of the following:

• Auto — When you set the Seed source, phase noise to Auto, seeds for each mixer instance are generated using a random number generator. The reset method of the instance has no effect.

• User specified — When you set the Seed source, phase noise to User specified, the value provided in the Seed for phase noise is used to initialize the random number generator and the reset method resets the random number generator using the Seed for phase noise property value.

Dependencies

To enable this parameter, select the Include phase noise parameter.

Seed for phase noise — Seed for random number generator

67987 (default) | nonnegative integer less than 2³²

Seed for the random number generator, specified as a nonnegative integer less than 2³². Use this value to initialize the random number generator.

Dependencies

To enable this parameter, select Include phase noise and set the Seed source, phase noise parameter to User specified.

Plot phase characteristics — Plot phase characteristics

button

This button plots the phase characteristics based on the parameters specified on the Noise tab and either the block sample time when a simulation has been performed or estimated from the Frequency offset (Hz) parameter values.

For more information, see Plot Phase Noise Characteristics.

Algorithms

Mixer Architectures and Design Equations

Architectural models for the Mixer block are shown here. Mixer and phase noise for all cases are included here.

Modulator and Demodulator Architectures and Equations

Modulator and demodulator architectures includes system noise, phase noise, and nonlinear polynomials to translates the carrier. A random number generator is used as an input to generate phase noise.

The output of the ideal modulator and demodulator circuit with nonlinearities, Y_out, is given by this equation.

$${\text{Y}}_{\text{out}}\text{ = }\left({\text{c}}_{\text{1}}\text{ + (3×}\frac{{\text{c}}_{\text{3}}}{\text{4}}\text{)) × }{\left|{\text{X}}_{\text{M}}\right|}^{\text{2}}\right)\text{ × }\left|{\text{X}}_{\text{M}}\right|\text{ × exp}\left({\text{i × angle(X}}_{\text{M}}\text{)}\right)$$

where,

$$\begin{array}{l}{\text{X}}_{\text{M}}{\text{ = (I}}_{\text{N}}{\text{ × c}}_{\text{Ph}}{\text{- Q}}_{\text{N}}{\text{×s}}_{\text{Ph}}{\text{) + j (Q}}_{\text{N}}{\text{ × c}}_{\text{Ph}}{\text{ - I}}_{\text{N}}{\text{ × s}}_{\text{Ph}}\text{)}\\ {\text{c}}_{\text{Ph}}\text{ = cosd(phaseOffset(deg) + phaseNoise(deg))}\\ {\text{s}}_{\text{Ph}}\text{ = sind(phaseOffset(deg) + phaseNoise(deg))}\\ {\text{I}}_{\text{N}}{\text{ + jQ}}_{\text{N}}{\text{= (I}}_{\text{in}}{\text{ + jQ}}_{\text{in}}\text{) + System Noise}\end{array}$$

The nonlinear polynomial coefficients, c₁ and c₃ , are provided in Nonlinearities in Idealized Baseband Mixer Block.

IQ Modulator Architecture and Equations

The IQ modulator primary consists of two mixers, f_I() and f_Q(). The Mixers convert baseband signals to RF signals and are commonly used in direct conversion architectures. The f_I() and f_Q(), are responsible for introducing gain, gain imbalance, phase imbalance, and nonlinearities into the IQ demodulator.

The output of IQ Modulator, Y_out, is given as

$${\text{Y}}_{\text{out}}\text{ = }\left({\text{I}}_{\text{out}}\text{ × cosd}\left({\text{I}}_{\text{Offset}}\right){\text{ + Q}}_{\text{out}}\text{ × sind}\left({\text{Q}}_{\text{offset}}\right)\right)\text{ - i}\left({\text{I}}_{\text{out}}\text{ × sind}\left({\text{I}}_{\text{Offset}}\right){\text{ - Q}}_{\text{out}}\text{ × cosd}\left({\text{Q}}_{\text{offset}}\right)\right)$$

where,

$$\begin{array}{l}{\text{I}}_{\text{out}}{\text{ = (c}}_{\text{1}}\text{ + }\frac{{\text{3c}}_{\text{3}}}{\text{4}}{\text{ × I}}_{\text{N}}^{\text{2}}{\text{) × I}}_{\text{N}}\\ {\text{Q}}_{\text{out}}{\text{ = (c}}_{\text{1Q}}\text{ + }\frac{{\text{3c}}_{\text{3Q}}}{\text{4}}{\text{ × Q}}_{\text{N}}^{\text{2}}{\text{) × Q}}_{\text{N}}\\ {\text{I}}_{\text{offset}}\text{ = }\frac{\text{phaseNoise(deg) + phaseImbalance (deg)}}{\text{2}}\\ {\text{Q}}_{\text{offset}}\text{= }\frac{\text{phaseNoise(deg) - phaseImbalance (deg)}}{\text{2}}\end{array}$$

The nonlinear polynomial coefficient c₃ are provided in Nonlinearities in Idealized Baseband Mixer Block. The modulators linear gains are c₁ and c_1Q are provided in this equation.

$$\begin{array}{l}{\text{c}}_{\text{1}}{\text{ = (1 + δ) × 10}}^{\text{(ConversionGainDB/20)}}\\ {\text{c}}_{\text{1Q}}{\text{= (1 - δ) × 10}}^{\text{(ConversionGainDB/20)}}\end{array}$$

where,

$$\text{δ = }\frac{{\text{10}}^{\text{(GainImbalanceDB / 20)}}\text{ - 1}}{{\text{10}}^{\text{(GainImbalanceDB / 20)}}\text{ + 1}}$$

IQ Demodulator Architecture and Equations

The architecture of an IQ demodulator is given below. The in-phase, I_out, and quadrature component, Q_out, of the modulated signal are the output of the f_I() and f_Q(), respectively. The mixers, f_I() and f_Q() are responsible for introducing gain, gain imbalance, phase imbalance, and nonlineatites into the IQ demodulator.

The output of the IQ Demodulator, Y_out, is given as

$${\text{Y}}_{\text{out}}{\text{ = I}}_{\text{α}}{\text{ × sqrt(P}}_{\text{I}}{\text{) × cosd(Theta - I}}_{\text{offset}}{\text{) + iQ}}_{\text{α}}{\text{ × sqrt(P}}_{\text{Q}}{\text{) × sind(Theta - Q}}_{\text{offset}}\text{)}$$

where,

$$\begin{array}{l}{\text{I}}_{\text{α}}{\text{ = (c}}_{\text{1}}\text{ + }\frac{{\text{3c}}_{\text{3}}}{\text{4}}{\text{ × P}}_{\text{IN}}\text{)}\\ {\text{Q}}_{\text{α}}{\text{ = (c}}_{\text{1Q}}\text{ + }\frac{{\text{3c}}_{\text{3Q}}}{\text{4}}{\text{ × P}}_{\text{Q}}\text{)}\\ {\text{I}}_{\text{offset}}\text{ = }\frac{\text{phaseNoise(deg) + phaseImbalance (deg)}}{\text{2}}\\ {\text{Q}}_{\text{offset}}\text{ = }\frac{\text{phaseNoise(deg) - phaseImbalance (deg)}}{\text{2}}\\ \text{Theta = angle(Sig)}\\ {\text{P}}_{\text{IN}}\text{ = }{\left|\text{Sig}\right|}^{\text{2}}\\ {\text{P}}_{\text{I}}{\text{ = f (P}}_{\text{IN}}\text{, (1 + GainImbalance))}\\ {\text{P}}_{\text{Q}}{\text{ = f (P}}_{\text{IN}}\text{, (1 - GainImbalance))}\end{array}$$

The nonlinear polynomial coefficient c₃ are provided in Nonlinearities in Idealized Baseband Mixer Block. The modulators linear gains c₁ and c_1Q are provided in this equation.

$$\begin{array}{l}{\text{c}}_{\text{1}}{\text{ = (1 + δ) × 10}}^{\text{(ConversionGainDB/20)}}\\ {\text{c}}_{\text{1Q}}{\text{= (1 - δ) × 10}}^{\text{(ConversionGainDB/20)}}\end{array}$$

where,

$$\text{δ = }\frac{{\text{10}}^{\text{(GainImbalanceDB / 20)}}\text{ - 1}}{{\text{10}}^{\text{(GainImbalanceDB / 20)}}\text{ + 1}}$$

Mixer Sidebands

Upper and Lower Sidebands

The expression for S_out shows the production of upper and lower sidebands, (ω_lo+ω_in) and (ω_lo−ω_in), and the effect of the difference values of the input carrier and LO signal on the sine function. Applying the trigonometric identity

$$\text{cos}\left(\alpha +\beta \right)=\text{ cos}\left(\alpha \right)\times \text{cos}\left(\beta \right)–\text{ sin}\left(\alpha \right)\times \text{sin}\left(\beta \right)$$

to the a mixer product expression, S_out = S_inx S_lo yields

$$\begin{array}{l}{S}_{\text{out}}={\text{ S}}_{in}\times {\text{ S}}_{lo}\\ =\left({\text{A}}_{in}\left(\text{t}\right)\times \text{cos }\left({\omega }_{in}\text{t}\right)\right)\times \left({\text{A}}_{lo}\left(\text{t}\right)\times \text{cos }\left({\omega }_{lo}\text{t}+\varphi \left(\text{t}\right)\right)\right)\\ \text{ = }\left(\frac{{\text{A}}_{in}\left(\text{t}\right)\times {\text{A}}_{lo}\left(\text{t}\right)}{2}\right)\text{ x }\left\{\begin{array}{l}\text{cos}\left(\varphi \left(\text{t}\right)\right)\times \text{cos}\left({\omega }_{lo}+{\omega }_{in}\right)\text{t }-\text{ sin}\left(\varphi \left(\text{t}\right)\right)\times \text{sin}\left({\omega }_{lo}+{\omega }_{in}\right)\text{t}\\ +\text{cos}\left(\varphi \left(\text{t}\right)\right)\times \text{cos}\left({\omega }_{lo}-{\omega }_{in}\right)\text{t}-\text{sin}\left(\varphi \left(\text{t}\right)\right)\times \text{sin}\left({\omega }_{lo}-{\omega }_{in}\right)\text{t}\end{array}\right\}\\ \end{array}$$

where, the term connected to the higher output frequency, ω_in+ω_lo, is the upper sideband and |ω_lo-ω_in| is the lower sideband. Since Ideal Baseband library blocks only support a single carrier signal, the desired output sideband must be selected. Set the Mixer sideband parameter to Modulator.

For demodulators, only the lower sideband can be used as an output. Finally select the Input carrier frequency greater than LO frequency parameter when the term sin(ω_lo-ω_in) contributes to the output signal.

Mixer Selections by Type

When selecting a Mixer type, this table provides the available sideband options LO phase offset (deg), I/Q gain imbalance (dB), and I/Q phase imbalance (deg). In addition, specify the relative size of RF to LO when the output frequency depends on the sign of (RF–LO).

Mixer Type	Sideband	If RF > LO	Impairments
Modulator	Higher	N.A	LO phase offset
Modulator	Lower	Select the Input carrier frequency greater than LO frequency parameter	LO phase offset
Demodulator	N.A	N.A	LO phase offset

Mixer Block Icons

This table shows you how the icons on this block will vary based on how you set the Parameters on the block.

Mixer Type	Include Mixer Noise	Include Phase Noise: off	Include Phase Noise: on
Modulator	off
	on
Demodulator	off
	on
IQ Modulator	off
	on
IQ Demodulator	off
	on

Note

After you set the block parameters you must click the Apply button to see the icon change.

References

[1] Razavi, Behzad. “Basic Concepts “ in RF Microelectronics, 2nd edition, Prentice Hall, 2012.

[2] Kundert, Ken.“ Accurate and Rapid Measurement of IP₂ and IP₃,“ The Designer Guide Community, May 22, 2002.

[3] 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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a

R2023a: Phase noise characteristics of Mixer block changed

Starting in this release, the extrapolated low-frequency phase noise below the first frequency point that specifies the 1/f^3 in the Mixer block is now 30 dB/decade instead of 3 dB/decade.

When you open a model created before R2023a containing the Mixer block and click the Plot Phase Characteristics button, the software scales the phase noise level in dBc/Hz on the y-axis in a phase noise magnitude response plot.

For example, open the Mixer block and select Include Phase Noise. Set the Number of signal samples to 2^10 and click the Apply button. Click the Plot Phase Characteristics button to plot the phase noise magnitude response and observe that the first frequency point that specifies the 1/f^3 in the Mixer block is scaled to 30 dB/decade.

R2021a: Mixer models and noise supported for Mixer block in Idealized Baseband library changed

Starting in R2021a, the Mixer block supports modulator, demodulator, IQ modulator, and IQ demodulator mixers with impairments and noise. The new Mixer block enables you to use pre-R2021a functionality when the Mixer type parameter is set to Modulator.

When you open a model from a previous release containing the Mixer block from the Idealized Baseband library, the pre-R2021a version of this block is automatically replaced with the R2021a version of this block with impairments and noise.