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Model RF to RF demodulator

**Library:**RF Blockset / Circuit Envelope / Systems

The Demodulator block models an RF to RF demodulator.

`Source of conversion gain`

— Source parameter of conversion gain`Available power gain`

(default) | `Open circuit voltage gain`

| `Polynomial coefficients`

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

`Available power gain`

— Relates the ratio of power of a single sideband (SSB) at the output to the input power. This calculation assumes a matched load and source termination.`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.

`Available power gain`

— Ratio of power of SSB at the output to input power `0 dB`

(default) | scalar in dB or a unitless ratioRatio of power of SSB at output to input power, specified as a scalar
in dB or a unitless ratio. For a unitless ratio, select
**None**.

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

.

`Open circuit voltage gain`

— Open circuit voltage gain`0 dB`

(default) | scalar Open circuit voltage gain, specified as a scalar in dB.

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

.

`Polynomial coefficients`

— Coefficients of polynomial specifying voltage gain`[0 1]`

(default) | vectorPolynomial 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,
`[`

,
the polynomial it represents is:`a`

_{0},`a`

_{1},`a`

_{2},
... `a`

_{9}]

*V _{out}* =

For example, the vector
`[`

specifies the relation `a`

_{0},`a`

_{1},`a`

_{2},`a`

_{3}]*V _{out}* =

`[``a`

_{0},`a`

_{1},`a`

_{2}]

defines the same polynomial as
`[``a`

_{0},`a`

_{1},`a`

_{2},
0]

. The default value is `[0,1]`

, corresponding to the
linear relation *V _{out}* =

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

.

`Local oscillator frequency`

— Local oscillator (LO) frequency`0`

`Hz`

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

`Input impedance (Ohm)`

— Input impedance of demodulator`50`

(default) | scalar Input impedance of demodulator, specified as a scalar in Ohms.

`Output impedance (Ohm)`

— Output impedance of demodulator`50 `

(default) | scalar Output impedance of demodulator, specified as a scalar in Ohms.

`Add Image Reject filter`

— Image reject (IR) filter parameters`off`

(default) | `on`

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

`Add Channel Select filters`

— Channel select (CS) filter parameters`off`

(default) | `on`

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

`Ground and hide negative terminals`

— Ground and hide negative circuit terminals`on`

(default) | `off`

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.

`Edit System`

— Break demodulator block links and replace internal variables by appropriate valuesbutton

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

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

`LO to In isolation`

— Ratio of magnitude between LO voltage to leaked voltage at input port
(RF)`inf`

`dB`

(default) | scalarRatio of magnitude of LO voltage to leaked voltage at input port (RF), specified as a scalar in dB.

`Noise figure (dB)`

— Signal-to-noise ratio (SNR) between outputs and input `0`

(default) | scalarSingle-sideband noise figure of mixer, specified as a scalar in dB.

To model noise in a circuit envelope model with a
Demodulator block, you must select the
**Simulate noise** check box in the Configuration block dialog
box.

`Add phase noise`

— Add phase noise`off`

(default) | `on`

Select this parameter to add phase noise to your demodulator system.

`Phase noise frequency offset (Hz)`

— Phase noise frequency offset`1`

(default) | scalar | vector | matrixPhase 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.

To enable this parameter, select **Add phase
noise**.

`Phase noise level (dBc/Hz)`

— Phase noise level`-Inf`

(default) | scalar | vector | matrixPhase noise level, specified as a scalar, vector, or matrix with element 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.

To enable this parameter, select **Add phase
noise**.

`Automatically estimate impulse response duration`

— Automatically estimate impulse response duration`on`

(default) | `off`

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

`Impulse response duration`

— Impulse response duration```
1e-10
```

`s`

(default) | scalarImpulse 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

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

Selecting `Polynomial coefficients`

for
**Source of conversion gain** in the
**Main** tab removes the
**Nonlinearity** parameters.

`Nonlinear polynomial type`

— Polynomial nonlinearity`Even and odd order`

(default) | `Odd order`

Polynomial nonlinearity, specified as one of the following:

`Even and odd order`

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

: The Demodulator generates only "odd-order" intermodulation frequencies.The linear gain determines the linear

*a*_{1}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`

— Intercept points convention`Input`

(default) | `Output`

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**.

`IP2`

— Second-order intercept point`inf`

`dBm`

(default) | scalar Second-order intercept point, specified as a scalar in dBm, W, mW, or
dBW. The default value, `inf dBm`

, corresponds to an
unspecified point.

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

.

`IP3`

— Third-order intercept point`inf dBm`

(default) | scalar 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`

— 1-dB gain compression power`inf dBM`

(default) | scalar1-dB gain compression power, specified as a scalar in dBm, W, mW, or dBW.

To set this parameter, select `Odd order`

in **Nonlinear polynomial type**.

`1-dB gain compression power`

— 1-dB gain compression power`inf dBM`

(default) | scalar1-dB gain compression power, specified as a scalar in dBm, W, mW, or dBW.

To set this parameter, select `Odd order`

in **Nonlinear polynomial type**.

`Gain compression at saturation`

— Gain compression at saturation`inf dBm`

(default) | scalarGain compression at saturation, specified as scalar in dBm, W, mW, or dBW.

When **Nonlinear polynomial type** is
`Odd order`

, specify the gain compression
at saturation.

To set this parameter, first select ```
Odd
order
```

in **Nonlinear polynomial
type**. Then, change the default value of
**Output saturation power**

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

`Design method`

— Simulation type`Ideal`

(default) | `Butterworth`

| `Chebyshev`

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

`Filter type`

— Filter type`Lowpass`

(default) | `Highpass`

| `Bandpass`

| `Bandstop`

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

`Implementation`

— Implementation`LC Tee`

| `LC Pi`

| `Transfer function`

| `Constant per carrier`

| `Frequency Domain`

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.`Frequency Domain`

: Model a ideal 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`

— Passband edge frequency`2 GHz`

(default) | scalarPassband edge frequency, specified as a scalar in Hz, kHz, MHz, or GHz.

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

and **Filter
type** to `Lowpass`

or
`Highpass`

.

`Implement using filter order`

— Implement using filter order`on`

(default) | `off`

Select this parameter to implement the filter order manually.

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

.

`Filter order`

— Filter order`3`

(default) | scalarFilter 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:

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

*R*_{p}is the passband ripple in dB.

To enable this parameter, select **Implement using filter
order** and set **Design method** to
`Butterworth`

or
`Chebyshev`

.

`Passband frequency`

— Passband frequency for lowpass and highpass filtersscalar

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

for `Lowpass`

filters and `2 GHz`

for
`Highpass`

filters.

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

and **Filter
type** to `Lowpass`

or
`Highpass`

.

`Passband frequencies`

— Passband frequencies for bandpass filters`[2 3] GHz`

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

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

and **Filter
type** to `Bandpass`

.

`Passband attenuation (dB)`

— Passband attenuation`10*log10(2)`

(default) | scalarPassband attenuation, specified as a scalar in dB. For bandpass filters, this value is applied equally to both edges of the passband.

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

.

`Stopband frequencies`

— Stopband frequencies for bandstop filters`[2.1 2.9]GHz`

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

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

and **Filter
type** to `Bandstop`

.

`Stopband edge frequencies`

— Stopband edge frequencies for ideal bandstop filters`[2.1 2.9] GHz`

(default) | 2-tuple vectorStopband 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.

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

and **Filter
type** to `Bandstop`

.

`Stopband attenuation (dB)`

— Stopband attenuation`40`

(default) | scalarStopband attenuation, specified as a scalar in dB. For bandstop filters, this value is applied equally to both edges of the stopband.

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

and **Filter
type** to `Bandstop`

.

`Source impedance (Ohm)`

— Input source resistance`50`

(default) | scalarInput source resistance, specified as a scalar in Ohms.

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

.

`Load impedance (Ohm)`

— Output load resistance`50`

(default) | scalarOutput load resistance, specified as a scalar in Ohms.

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

.

`Automatically estimate impulse response duration`

— Automatically estimate impulse response duration`on`

(default) | `off`

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

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

and
**Implementation** to ```
Frequency
domain
```

.

`Impulse response duration`

— Impulse response duration`1e-10`

`s`

(default) | scalarImpulse 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. The message also specifies the minimum duration suitable for the required resolution

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

`Export`

— Save filter design to a filebutton

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

and `.txt`

.

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

.

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

`Design method`

— Simulation type`Ideal`

(default) | `Butterworth`

| `Chebyshev`

** Filter type** and the model
specified in **Implementation**.

`Filter type`

— Filter type`Lowpass`

(default) | `Highpass`

| `Bandpass`

| `Bandstop`

**Design
method**.

`Implementation`

— Implementation`LC Tee`

| `LC Pi`

| `Transfer function`

| `Constant per carrier`

| `Frequency Domain`

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.`Frequency 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`

— Passband edge frequency`2 GHz`

(default) | scalarPassband edge frequency, specified as a scalar in Hz, kHz, MHz, or GHz.

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

.

`Implement using filter order`

— Implement using filter order`on`

(default) | `off`

Select this parameter to implement the filter order manually.

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

.

`Filter order`

— Filter order`3`

(default) | scalarFilter 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:

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

R

_{p}is the passband ripple in dB.

To enable this parameter, select **Implement using filter
order**.

`Passband frequency`

— Passband frequency for lowpass and highpass filtersscalar

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.

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

and **Filter
type** to `Lowpass`

or
`Highpass`

.

`Passband frequencies`

— Passband frequencies for bandpass filters`[2 3] GHz`

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

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

and **Filter
type** to `Bandpass`

.

`Passband attenuation (dB)`

— Passband attenuation`10*log10(2)`

(default) | scalarPassband attenuation, specified as a scalar in dB. For bandpass filters, this value is applied equally to both edges of the passband.

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

.

`Stopband frequencies`

— Stopband frequencies for bandstop filters`[2.1 2.9] GHz`

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

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

and **Filter
type** to `Bandstop`

.

`Stopband edge frequencies`

— Stopband edge frequencies for ideal bandstop filters`[2.1 2.9] GHz`

(default) | 2-tuple vectorStopband 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.

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

and **Filter
type** to `Bandstop`

.

`Stopband attenuation (dB)`

— Stopband attenuation`40`

(default) | scalarStopband attenuation, specified as a scalar in dB. For bandstop filters, this value is applied equally to both edges of the stopband.

**Design method**
to `Butterworth`

or
`Chebyshev`

and **Filter
type** to `Bandstop`

.

`Source impedance (Ohm)`

— Input source resistance`50`

(default) | scalarInput source resistance, specified as a scalar in 0hms.

`Load impedance (Ohm)`

— Output load resistance`50`

(default) | scalarOutput load resistance, specified as a scalar in Ohms.

`Automatically estimate impulse response duration`

— Automatically estimate impulse response duration`on`

(default) | `off`

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

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

and
**Implementation** to ```
Frequency
domain
```

.

`Impulse response duration`

— Impulse response duration`1e-10`

`s`

(default) | scalarImpulse 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. The message also specifies the minimum duration suitable for the required resolution

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

`Export`

— Save filter design to a filebutton

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

and `.txt`

.

To enable this parameter, set **Design method**
to `Butterworth`

or
`Chebyshev`

.

[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.

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