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# IQ Modulator

Convert baseband signal to RF signal

• Library:
• RF Blockset / Circuit Envelope / Systems

## Description

The `IQ Modulator` converts a baseband signal to RF signal and models an IQ modulator with impairments. `I` stands for the in-phase component of the signal and `Q` stands for the quadrature phase component of the signal. You can use the IQ Modulator to design direct conversion transmitters.

## Parameters

expand all

### Main

Source parameter of conversion gain, specified as one of the following:

• `Available power gain` — Relates the ratio of the power of a single sideband (SSB) of the output to the input power at the `I` branch. This assumes no gain mismatch and that the input at the Q branch is Qin = - j.Iin

• `Open circuit voltage gain` — Value of the open circuit voltage gain parameter as the linear voltage gain term of the polynomial voltage-controlled voltage source (VCVS).

• `Polynomial coefficients` — Implements a nonlinear voltage gain according to the polynomial you specify.

Ratio of the power of SSB at the output to input power at `I` branch, specified as a scalar in dB or a unitless ratio. For a unitless ratio, select `None`.

#### Dependencies

To enable this parameter, set Source of conversion gain to ```Available power gain```.

Open circuit voltage of IQ modulator, specified as a scalar in dB or a unitless ratio. For a unitless ratio, select `None`.

#### Dependencies

To enable this parameter, set Source of conversion gain to ```Open circuit voltage gain```.

Polynomial coefficients, specified as a vector.

The order of the polynomial must be less than or equal to 9. The coefficients must be ordered in ascending powers. If a vector has 10 coefficients, ```[a0,a1,a2, ... a9]```, the polynomial it represents is:

Vout = a0 + a1Vin + a2Vin2 + ...  + a9Vin9

a1 represents the linear gain term, and higher-order terms are modeled according to [2].

For example, the vector `[a0,a1,a2,a3]` specifies the relation Vout = a0 + a1V1 + a2V12 + a3V13. Trailing zeros are omitted. So `[a0,a1,a2]` defines the same polynomial as ```[a0,a1,a2, 0]```.

By default, the value is [0,1], corresponding to the linear relation Vout = Vin.

#### Dependencies

To enable this parameter, set Source of conversion gain to ```Polynomial coefficients```.

Local oscillator (LO) frequency, specified as a scalar in Hz, kHz, MHz, or GHz.

Input impedance of IQ modulator, specified as a scalar in Ohms.

Output impedance of IQ modulator, specified as a scalar in Ohms.

Select to add the IR filter parameter tab. Clear to remove the tab.

Select to add the CS filter parameter tab. Clear to remove the tab.

Select to internally ground and hide the negative terminals. Clear to expose the negative terminals. When the terminals are exposed, you can connect them to other parts of your model.

Use this button to break IQ modulator links to the library. The internal variables are replaced by their values which are estimated using IQ modulator parameters. The IQ Modulator becomes a simple subsystem masked only to keep the icon.

Use to edit the internal variables without expanding the subsystem. Use to expand the subsystem in the Simulink™ canvas and to edit the subsystem.

### Impairments

Gain difference between `I` and `Q` branches, specified as a scalar in dB, or a unitless ratio. Gain mismatch is assumed to be forward-going, that is, the mismatch does not affect leakage from LO to RF.

If the gain mismatch is specified, the value $\left(Available\text{ }\text{\hspace{0.17em}}power\text{\hspace{0.17em}}gain+I/Q\text{\hspace{0.17em}}gain\text{\hspace{0.17em}}mismatch\right)$ relates the ratio of power of the single-sideband (SSB) at the `Q` input branch to the output power.

Phase difference between `I` and `Q` branches, specified as a scalar in degrees or radians. This mismatch affects the LO to input RF leakage.

Ratio of magnitude between LO voltage to leaked RF voltage, specified as a scalar in dB, or a unitless ratio. For a unitless ratio, select `None`.

Single-sided noise power spectral distribution, specified as a scalar in dBm/Hz. This block assumes -174dBm/Hz noise input at both `I` and `Q` branches.

Select this parameter to add phase noise to your IQ modulator system.

Phase noise frequency offset, specified as a scalar, vector, or matrix with each element unit in Hz.

If you specify a matrix, each column corresponds to a non-DC carrier frequency of the CW source. The frequency offset values bind the envelope bandwidth of the simulation. For more information, see Configuration.

#### Dependencies

To enable this parameter, select Add phase noise.

Phase noise level, specified as a scalar, vector, or matrix with element unit in dBc/Hz.

If you specify a matrix, each column corresponds to a non-DC carrier frequency of the CW source. The frequency offset values bind the envelope bandwidth of the simulation. For more information, see Configuration.

#### Dependencies

To enable this parameter, select Add phase noise.

Select to automatically estimate impulse response for phase noise. Clear to specify the impulse response duration using Impulse response duration.

Impulse response duration used to simulate phase noise, specified as a scalar in s, ms, us, or ns.

### Note

The phase noise profile resolution in frequency is limited by the duration of the impulse response used to simulate it. Increase this duration to improve the accuracy of the phase noise profile. A warning message appears if the phase noise frequency offset resolution is too high for a given impulse response duration. This message also specifies the minimum duration suitable for the required resolution.

#### Dependencies

To set this parameter, clear Automatically estimate impulse response duration.

### Nonlinearity

Selecting `Polynomial coefficients` for Source of conversion gain in the Main tab removes the Nonlinearity parameters.

Polynomial nonlinearity, specified as one of the following:

• `Even and odd order`: The IQ Modulator can produce second-order and third-order intermodulation frequencies, in addition to a linear term.

• `Odd order`: The IQ Modulator generates only "odd-order" intermodulation frequencies.

The linear gain determines the linear a1 term. The block calculates the remaining terms from the values specified in IP3, 1-dB gain compression power, Output saturation power, and Gain compression at saturation. The number of constraints you specify determines the order of the model. The figure shows the graphical definition of the nonlinear IQ modulator parameters.

Intercept points convention, specified as `Input` (input-referred) or `Output` (output-referred). Use this specification for the intercept points IP2, IP3, the 1-dB gain compression power, and the Output saturation power.

Second-order intercept point, specified as a scalar in dBm, W, mW, or dBW. The default value `inf` `dBm` corresponds to an unspecified point.

#### Dependencies

To enable this parameter, set Nonlinear polynomial type to ```Even and odd order```.

Third-order intercept point, specified as a scalar in dBm, W, mW, or dBW. The default value `inf` `dBm` corresponds to an unspecified point.

#### Dependencies

To enable this parameter, set Nonlinear polynomial type to ```Even and odd order```.

1-dB gain compression power, specified as a scalar in dBm, W, mW, or dBW. The 1-dB gain compression point must be less than the output saturation power.

#### Dependencies

To enable this parameter, set `Odd order` in Nonlinear polynomial type tab.

Output saturation power, specified as a scalar. The block uses this value to calculate the voltage saturation point used in the nonlinear model. In this case, the first derivative of the polynomial is zero, and the second derivative is negative.

#### Dependencies

To enable this parameter, set `Odd order` in Nonlinear polynomial type tab.

Gain compression at saturation, specified as a scalar.

#### Dependencies

To enable this parameter, first select ```Odd order``` in Nonlinear polynomial type tab. Then change the default value of Output saturation power .

### IR Filter

Select Add Image Reject filters in the Main tab to see the IR Filter parameters tab.

Simulation type. Simulates an ideal, Butterworth, or Chebyshev filter of the type specified in Filter type and the model specified in Implementation.

Filter. Simulates a lowpass, highpass, bandpass, or bandstop filter type of the design specified in Design method

Implementation, specified as one of the following:

• `LC Tee`: Model an analog filter with an LC lumped Tee structure when the Design method is Butterworth or Chebyshev.

• `LC Pi`: Model an analog filter with an LC lumped Pi structure when the Design method is Butterworth or Chebyshev.

• `Transfer Function`: Model an analog filter using two-port S-parameters when the Design method is Butterworth or Chebyshev.

• `Constant per carrier`: Model a filter with either full transmission or full reflection set as constant throughout the entire envelope band around each carrier. The Design method is specified as ideal.

• `Filter Domain`: Model a filter using convolution with an impulse response. The Design method is specified as ideal. The impulse response is computed independently for each carrier frequency to capture the ideal filtering response. When a transition between full transmission and full reflection of the ideal filter occurs within the envelope band around a carrier, the frequency-domain implementation captures this transition correctly up to a frequency resolution specified in Impulse response duration.

### Note

Due to causality, a delay of half the impulse response duration is included for both reflected and transmitted signals. This delay impairs the filter performance when the Source and Load resistances differ from the values specified in filter parameters.

By default, the Implementation is `Constant per carrier` for an ideal filter and `LC Tee` for Butterworth or Chebyshev.

Passband edge frequency, specified as a scalar in Hz, kHz, MHZ, or GHz.

#### Dependencies

To enable this parameter, set Design method to `Ideal` and Filter type to `Lowpass` or `Highpass`.

Select this parameter to implement the filter order manually.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev`.

Filter order, specified as a scalar. For a Filter type of `Lowpass` or `Highpass`, the filter order is the number of lumped storage elements. For a Filter type of `Bandpass` of `Bandstop`, the number of lumped storage elements is twice the filter order.

### Note

For even order Chebyshev filters, the resistance ratio $\frac{{R}_{\text{load}}}{{R}_{\text{source}}}>{R}_{\text{ratio}}$ for Tee network implementation and $\frac{{R}_{\text{load}}}{{R}_{\text{source}}}<\frac{1}{{R}_{\text{ratio}}}$ for Pi network implementation.

`${R}_{\text{ratio}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{\sqrt{1+{\epsilon }^{2}}+\epsilon }{\sqrt{1+{\epsilon }^{2}}-\epsilon }$`

where:

• `$\epsilon \text{\hspace{0.17em}}=\text{\hspace{0.17em}}\sqrt{{10}^{\left(0.1{R}_{\text{p}}\right)}-1}$`

• Rp is the passband ripple in dB.

#### Dependencies

To enable this parameter, select Implement using filter order.

Passband frequency for lowpass and highpass filters, specified as a scalar in Hz, kHz, MHz, or GHz. The default value is ```1 GHz``` for `Lowpass` filters and `2 GHz` for `Highpass` filters.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev` and Filter type to `Lowpass` or `Highpass`.

Passband frequencies for bandpass filters, specified as a 2-tuple vector in Hz, kHz, MHz, or GHz. This option is not available for bandstop filters.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev` and Filter type to `Bandpass`.

Passband attenuation, specified as a scalar in dB. For bandpass filters, this value is applied equally to both edges of the passband.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev`.

Stopband frequencies for bandstop filters, specified as a 2-tuple vector in Hz, kHz, MHz, or GHz. This option is not available for bandpass filters.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev` and Filter type to `Bandstop`.

Stopband edge frequencies for bandstop filters, specified as a 2-tuple vector in Hz, kHz, MHz, or GHz. This option is not available for ideal bandpass filters.

#### Dependencies

To enable this parameter, set Design method to `Ideal` and Filter type to `Bandstop`.

Stopband attenuation, specified as a scalar in dB. For bandstop filters, this value is applied equally to both edges of the stopband.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev` and Filter type to `Bandstop`.

Input source resistance, specified as a scalar in Ohms.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev`.

Output load resistance, specified as a scalar in Ohms.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev`.

Select to automatically estimate impulse response for phase noise. Clear to manually specify the impulse response duration using Impulse response duration.

#### Dependencies

To enable this parameter, set Design method to `Ideal` and Implementation to ```Frequency domain```.

Impulse response duration used to simulate phase noise, specified as a scalar in s, ms, us, or ns. You cannot specify impulse response if the amplifier is nonlinear.

### Note

The phase noise profile resolution in frequency is limited by the duration of the impulse response used to simulate it. Increase this duration to improve the accuracy of the phase noise profile. A warning message appears if the phase noise frequency offset resolution is too high for a given impulse response duration. This message also specifies the minimum duration suitable for the required resolution

#### Dependencies

To enable this parameter, clear Automatically estimate impulse response duration.

Use this button to save filter design to a file. Valid file types are `.mat` and `.txt`.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev`.

### CS Filter

Select Add Channel Select filter in the Main tab to see the CS Filter parameters.

Simulation type. Simulates an ideal, Butterworth, or Chebyshev filter of the type specified in Filter type and the model specified in Implementation.

Filter. Simulates a lowpass, highpass, bandpass, or bandstop filter type of the design specified in Design method.

Implementation, specified as one of the following:

• `LC Tee`: Model an analog filter with an LC lumped Tee structure when the Design method is Butterworth or Chebyshev.

• `LC Pi`: Model an analog filter with an LC lumped Pi structure when the Design method is Butterworth or Chebyshev.

• `Transfer Function`: Model an analog filter using two-port S-parameters when the Design method is Butterworth or Chebyshev.

• `Constant per carrier`: Model a filter with either full transmission or full reflection set as constant throughout the entire envelope band around each carrier. The Design method is specified as ideal.

• `Filter Domain`: Model a filter using convolution with an impulse response. The Design method is specified as ideal. The impulse response is computed independently for each carrier frequency to capture the ideal filtering response. When a transition between full transmission and full reflection of the ideal filter occurs within the envelope band around a carrier, the frequency-domain implementation captures this transition correctly up to a frequency resolution specified in Impulse response duration.

### Note

Due to causality, a delay of half the impulse response duration is included for both reflected and transmitted signals. This delay impairs the filter performance when the Source and Load resistances differ from the values specified in filter parameters.

By default, the Implementation is `Constant per carrier` for an ideal filter and `LC Tee` for Butterworth or Chebyshev.

Passband edge frequency, specified as a scalar in Hz, kHz, MHz, or GHz.

#### Dependencies

To enable this parameter, set Design method to `Ideal`.

Select this parameter to implement the filter order manually.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev`.

Filter order, specified as a scalar. This order is the number of lumped storage elements in `lowpass` or `highpass`. In `bandpass` or `bandstop`, the number of lumped storage elements are twice the value.

### Note

For even order Chebyshev filters, the resistance ratio $\frac{{R}_{\text{load}}}{{R}_{\text{source}}}>{R}_{\text{ratio}}$ for Tee network implementation and $\frac{{R}_{\text{load}}}{{R}_{\text{source}}}<\frac{1}{{R}_{\text{ratio}}}$ for Pi network implementation.

`${R}_{\text{ratio}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{\sqrt{1+{\epsilon }^{2}}+\epsilon }{\sqrt{1+{\epsilon }^{2}}-\epsilon }$`

where:

• `$\epsilon \text{\hspace{0.17em}}=\text{\hspace{0.17em}}\sqrt{{10}^{\left(0.1{R}_{\text{p}}\right)}-1}$`

• Rp is the passband ripple in dB.

#### Dependencies

To enable this parameter, select Implement using filter order.

Passband frequency for lowpass and highpass filters, specified as a scalar in Hz, kHz, MHz, or GHz. By default, the passband frequency is `1 GHz` for `Lowpass` filters and `2 GHz` for `Highpass` filters.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev` and Filter type to `Lowpass` or `Highpass`.

Passband frequencies for bandpass filters, specified as a 2-tuple vector in Hz, kHz, MHz, or GHz. This option is not available for bandstop filters.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev` and Filter type to `Bandpass`.

Passband attenuation, specified as a scalar in dB. For bandpass filters, this value is applied equally to both edges of the passband.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev`.

Stopband frequencies for bandstop filters, specified as a 2-tuple vector in Hz, kHz, MHz, or GHz. This option is not available for bandpass filters.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev` and Filter type to `Bandstop`.

Stopband edge frequencies for bandstop filters, specified as a 2-tuple vector in Hz, kHz, MHz, or GHz. This option is not available for ideal bandpass filters.

#### Dependencies

To enable this parameter, set Design method to `Ideal` and Filter type to `Bandstop`.

Stopband attenuation, specified as a scalar in dB. For bandstop filters, this value is applied equally to both edges of the stopband.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev` and Filter type to `Bandstop`.

Input source resistance, specified as a scalar in Ohms.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev`.

Output load resistance, specified as a scalar in Ohms.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev`.

Select to automatically estimate impulse response for phase noise. Clear to specify the impulse response duration using Impulse response duration.

#### Dependencies

To enable this parameter, set Design method to `Ideal` and Implementation to ```Frequency domain```.

Impulse response duration used to simulate phase noise, specified as a scalar in s, ms, us, or ns. You cannot specify impulse response if the amplifier is nonlinear.

### Note

The phase noise profile resolution in frequency is limited by the duration of the impulse response used to simulate it. Increase this duration to improve the accuracy of the phase noise profile. A warning message appears if the phase noise frequency offset resolution is too high for a given impulse response duration. This message also specifies the minimum duration suitable for the required resolution

#### Dependencies

To set this parameter, clear Automatically estimate impulse response duration.

Use this button to save filter design to a file. Valid file types are `.mat` and `.txt`.

#### Dependencies

To enable this parameter, set Design method to `Butterworth` or `Chebyshev`.

## References

[1] Razavi, Behzad. RF Microelectronics. Upper Saddle River, NJ: Prentice Hall, 2011.

[2] Grob, Siegfried and Lindner, Jurgen, “Polynomial Model Derivation of Nonlinear Amplifiers”, Department of Information Technology, University of Ulm, Germany.