# Documentation

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# IQ Demodulator

Convert RF signal to baseband signal

• Library:
• RF Blockset / Circuit Envelope / Systems

## Description

The `IQ Demodulator` converts an RF signal to baseband signal. `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 Demodulator to design direct conversion receivers.

## Parameters

expand all

#### Main

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

• `Available power gain` — Relates the power of a single sideband (SSB) at the output `I` branch to the input power. If there is no gain mismatch, the gain at the `Q` branch matches the gain at the `I` branch.

• `Open circuit voltage gain` — Value of the open circuit voltage gain parameter as the linear voltage gain term of the polynomial VCVS.

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

Power of SSB at output to input power at `I`, specified as a scalar in dB or a unitless ratio, `None`.

#### Dependencies

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

Open circuit voltage gain, specified as a scalar in dB.

#### Dependencies

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

Order of polynomial, 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 Vo = a0 + a1V1 + a2V12 + a3V13. Trailing zeros are omitted, if a3 = 0, then `[a0,a1,a2]` defines the same polynomial as ```[a0,a1,a2, 0]```.

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

#### 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`. `0` Hz is not allowed.

Input impedance of demodulator, specified as a scalar.

Output impedance of demodulator, specified as a scalar.

Select this parameter to internally ground and hide the negative terminals. To expose the negative terminals, clear this parameter. By exposing these terminals, you can connect them to other parts of your model.

By default, this option is selected.

#### Impairments

Gain difference between `I` and `Q` branches, specified as a scalar in dB. 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 $Available\text{ }\text{\hspace{0.17em}}power\text{\hspace{0.17em}}gain+I/Q\text{\hspace{0.17em}}gain\text{\hspace{0.17em}}mismatch$ relates to the power of the single-sideband (SSB) at output the `Q` branch to the input power.

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

Ratio of magnitude between LO voltage to leaked RF voltage, specified as a scalar in dB. Phase accumulation in the path from LO input to the internal `I` and `Q` mixers (after phase shift and phase mismatch) and then to the RF is assumed to be zero.

Single-sideband noise figure of mixer, specified as a scalar.

To model noise in circuit envelope model with a Noise, Amplifier, or Mixer, IQ Demodulator block, you must select the Simulate noise check box in the Configuration block dialog box.

The following table summarizes the two competing definitions for specifying SSB noise, where the image frequency (IM) is defined as ωIM = ωLO + (ωLO – ωRF).

Noise ConventionSignal at RF FrequencySignal at IM FrequencyIQ Demodulator Block Supports This Model?
Single-sideband noise (SSB)S + N, signal with noiseN, noise onlyYes
IEEE definition of single-sideband noise (SSBIEEE)S + N, signal with noiseNo signalNo; you can create an equivalent model using an ideal filter created from an S-parameters block.

#### Nonlinearity

Polynomial nonlinearity, specified as one of the following:

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

• `Odd order`: The IQ Demodulator 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 demodulator parameters.

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

1-dB gain compression power, specified as a scalar. The 1-dB gain compression point must be less than the output saturation power.

#### Dependencies

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

Gain compression at saturation, specified as a scalar.

#### Dependencies

To enable this parameter, select `Odd order` in Nonlinear polynomial type tab and set Output saturation power .

## 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.