Mixer
Model mixer in RF systems
Libraries:
RF Blockset /
Circuit Envelope /
Elements
Description
The Mixer block performs signal frequency translation and nonlinear amplification.
For a given RF input signal, V_{RF} = A_{RF}cos(ω_{RF}t) and an LO input signal V_{LO} = Ac_{LO}cos(ω_{LO}t), the mixer multiplies the signals at the input ports:
$$\begin{array}{c}{V}_{\text{in}}{V}_{\text{LO}}={A}_{\text{in}}\mathrm{cos}\left({\omega}_{\text{in}}t\right){A}_{\text{LO}}\mathrm{cos}\left({\omega}_{\text{LO}}t\right)\\ =\frac{{A}_{\text{in}}{A}_{\text{LO}}}{2}\mathrm{cos}\left[\left({\omega}_{\text{in}}+{\omega}_{\text{LO}}\right)t\right]+\frac{{A}_{\text{in}}{A}_{\text{LO}}}{2}\mathrm{cos}\left[\left({\omega}_{\text{in}}{\omega}_{\text{LO}}\right)t\right]\end{array}$$
This mixing converts the frequency of RF signal to ω_{RF} + ω_{LO} and ω_{RF} – ω_{LO}. For the mixer to perform this operation correctly, you must include the frequencies ω_{RF} + ω_{LO} or ω_{RF} – ω_{LO} in the simulation frequencies the Configuration block calculates.
The Power gain specification for this block relates the power of a singlesideband (SSB) to the input.
After mixing the RF and LO signals, the mixer block performs amplification. To model linear amplification, the mixer scales the signals by the coefficient a_{1}. A Voltage Controlled Voltage Source (VCVS), specified with a polynomial, implements nonlinear amplification. The polynomial includes saturation automatically and produces additional intermodulation frequencies.
Mixer block mask icons are dynamic and indicate the current state of the applied noise parameter. This table shows you how the icons on this block vary based on the state of the Noise figure (dB) parameter on the block.
Noise figure (dB): 10  Noise figure (dB): 0 



Examples
Validating IP2/IP3 Using Complex Signals
Run a twotone experiment to measure the second and thirdorder intercept points of an amplifier.
Impact of Thermal Noise on Communication System Performance
Model thermal noise in a superheterodyne RF receiver and measure its effects on a communications system noise figure and bit error rate.
Create Virtual Connections Using Connection Label Block
Use a Connection Label block to create a virtual connection between two conserving ports.
Parameters
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
— The block uses the value of the Available power gain parameter to calculate the linear voltage gain term of the polynomial VCVS, a_{1}. This calculation assumes a matched load termination for the mixer.Open circuit voltage gain
— The block uses the value of the Open circuit voltage gain parameter as the linear voltage gain term of the polynomial VCVS, a_{1}.Polynomial coefficients
— The block implements a nonlinear voltage gain according to the polynomial you specify. The order of the polynomial must be less than or equal to 9 and the coefficients are ordered in ascending powers. If a vector a has 10 coefficients, [a_{0}, a_{1}, a_{2}, …, a_{9}], the polynomial it represents is V_{out} = a_{0} + a_{1} V_{in} + a_{2} V_{in}^{2}+ ⋯ + a_{9} V_{in}^{9}. In this case, a_{1} represents the linear gain term, and the modeling of higherorder terms is done according to [1].For example, the vector [a_{0}, a_{1}, a_{2}, a_{3}] specifies the relation V_{out} = a_{0} + a_{1} V_{in} + a_{2} V_{in}^{2} + ⋯ + a_{3} V_{in}^{3}.
Trailing zeroes are omitted: if a_{3} = 0, [a_{0}, a_{1}, a_{2}] defines the same polynomial as [a_{0}, a_{1}, a_{2}, 0]. The default value of this parameter is [0 1], corresponding to the linear relation V_{o} = V_{i}.
Available power gain — Linear gain of mixer
0 dB
(default)  scalar
Linear gain of mixer, specified as a scalar in dB. Specify the units from the corresponding dropdown list.
Dependencies
To enable this parameter, select Available power
gain
in Source of conversion gain tab.
Open circuit voltage gain — Open circuit voltage gain
0 dB
(default)  scalar
Open circuit voltage of mixer, specified as a scalar in dB. Specify the units from the corresponding dropdown list.
Dependencies
To enable this parameter, select Open circuit voltage
gain
in Source of conversion gain tab.
Polynomial coefficients — Order of polynomial
[0 1]
(default)  vector
Order of polynomial, specified as a vector.
The order of the polynomial must be less than or equal to 9. The coefficients are ordered in
ascending powers. If a vector has 10 coefficients,
[a_{0},a_{1},a_{2},
... a_{9}]
, the
polynomial it represents is:
V_{out} = a_{0} + a_{1}V_{in} + a_{2}V_{in}^{2} + ... + a_{9}V_{in}^{9}
where a_{1} represents
the linear gain term, and higherorder terms are modeled according
to [1].
For example, the vector
[a_{0},a_{1},a_{2},a_{32}]
specifies the relation V_{o} = a_{0} + a_{1}V_{1} + a_{2}V_{1}^{2} + a_{3}V_{1}^{3}. Trailing zeroes are omitted. If
a_{3} = 0, then
[a_{0},a_{1},a_{2}]
defines the same polynomial as
[a_{0},a_{1},a_{2},0].
The default value of this parameter is [0,1], corresponding to the linear
relation V_{o} =
V_{i}.
Dependencies
To enable this parameter, select Polynomial coefficients
in Source
of conversion gain tab.
Input impedance (Ohm) — Input impedance of mixer
50
(default)  scalar
Input impedance of mixer, specified as a scalar.
Output impedance (Ohm) — Output impedance of mixer
50
(default)  scalar
Output impedance of mixer, specified as a scalar.
LO impedance (Ohm) — Impedance at LO port of mixer
inf
(default)  scalar
Output impedance of mixer, specified as a scalar.
Noise figure (dB) — Singlesideband IEEE noise figure of mixer
0 dB
(default)  scalar
Singlesideband noise figure of mixer, specified as a scalar according to the IEEE^{®} definition.
To model noise in circuit envelope model with a Noise, Amplifier, or Mixer block, you must select the Simulate noise check box in the Configuration block dialog box.
The IEEE SSB definition assumes that the noise in the image bandwidth at the input of the mixer is perfectly rejected, while the mixer internally generates noise in both the image bandwidth and the signal bandwidth. As a result, the noise at the output of the mixer is the sum of two contributions:
$${N}_{\text{out}}={N}_{\text{in}}{G}_{\text{mix}}+2{N}_{\text{mixer}}{G}_{\text{mix}},$$
where:
N_{out} is the noise at the output of the mixer.
N_{in} is the noise at the input of the mixer (assuming that the noise in the image bandwidth is perfectly rejected).
N_{mixer} is the noise internally generated by the mixer in both the signal and the image bandwidths.
G_{mix} is the mixer gain.
As a result, the noise factor according to the IEEE SSB definition can be expressed as
$${F}_{\text{SSBIEEE}}=1+2{N}_{\text{mixer}}/{N}_{\text{in}},$$
which is related to other commonly used definitions through
$$\begin{array}{c}{F}_{\text{SSB}}=2+2{N}_{\text{mixer}}/{N}_{\text{in}}=1+{F}_{\text{SSBIEEE}},\\ {F}_{\text{DSB}}=1+{N}_{\text{mixer}}/{N}_{\text{in}}={\scriptscriptstyle \frac{1}{2}}\left(1+{F}_{\text{SSBIEEE}}\right).\end{array}$$
You can apply the IEEE SSB definition directly to describe mixer stages when using the Friis formulas for link budget analysis. Using the other definitions requires changing the Friis formulas. Both the Mixer block in RF Blockset™ and the RF Budget Analyzer app in RF Toolbox™ use the IEEE definition.
The analytic relationships between the three definitions allow you to simulate the noise level at the output of the mixer. For example,
$$\begin{array}{c}{F}_{\text{SSB}}=4\text{dB}\Rightarrow {F}_{\text{SSBIEEE}}=10{\mathrm{log}}_{10}({10}^{{F}_{\text{SSB}}/10}1)=1.79\text{dB},\\ {F}_{\text{DSB}}=4\text{dB}\Rightarrow {F}_{\text{SSBIEEE}}=10{\mathrm{log}}_{10}(2\times {10}^{{F}_{\text{DSB}}/10}1)=6.04\text{dB}\text{.}\end{array}$$
If you simulate an RF Blockset mixer without including an ideal image rejection filter, then the noise at the output of the mixer is larger than that predicted by the noise figure, because the noise in the image bandwidth is effectively folded onto the output signal.
For this reason, when generating models, both the Modulator and Demodulator blocks insert an ideal imagerejection filter automatically. (You can remove the filtering within the block mask.)
The Noise Figure Testbench block measures the SSB noise figure and enables you to verify that the simulated noise figure has the expected value.
If you add an ideal image rejection filter to your model, then the effective noise figure is consistent with the analytic value.
If you remove the imagerejection filter, or if you use a filter with partial rejection, then the measured noise figure is larger than the analytic value.
Ground and hide negative terminals — Ground RF circuit terminals
on
(default)  off
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.
Nonlinear polynomial type — Polynomial nonlinearity
Even and odd order
(default)  Odd order
Polynomial nonlinearity, specified as one of the following:
Even and odd order
: When you selectEven and odd order
, the amplifier can produce second and thirdorder intermodulation frequencies in addition to a linear term.Odd order
: When you selectOdd order
, the amplifier generates only odd order intermodulation frequencies.The linear gain determines the linear a_{1} term. The block calculates the remaining terms from the specified parameters. These parameters are IP3, 1dB 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 mixer parameters.
Intercept points convention — Intercept points convention
Output
(default)  Input
Intercept points convention, specified as Input
referred
or Output
referred. Use this specification
for the intercept points, 1dB gain compression power, and saturation
power.
IP2 — Secondorder intercept point
inf
dBm
(default)  scalar
Secondorder intercept point. specified as a scalar. The default
value inf
dBm
corresponds
to an unspecified point.
Dependencies
To enable this parameter, select Even and odd order
in Nonlinear
polynomial type tab.
IP3 — Thirdorder intercept point
inf
dBm
(default)  scalar
Thirdorder intercept point, specified as a scalar. The default
value inf
dBm
corresponds
to an unspecified point.
1dB gain compression power — 1dB gain compression power
inf
dBm
(default)  scalar
1dB gain compression power, specified as a scalar. The 1dB 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 — Output saturation power
inf
dBm
(default)  scalar
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 — Gain compression at saturation
inf
dBm
(default)  scalar
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] Grob, Siegfried, and Jürgen Lindner. “Polynomial Model Derivation of Nonlinear Amplifiers.” Department of Information Technology, University of Ulm, Germany.
Version History
Introduced in R2010bR2021b: Mixer block icon updated
Starting in R2021b, the Mixer block icon has updated. The block icons are now dynamic and show the current state of the noise parameter.
When you open a model created before R2021b containing a Mixer block, the software replaces the block icon with the R2021b version.
See Also
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