Matlab SIMRF 3 user guide

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SimRF™ 3

User’s Guide

Page 2

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SimRF™ User’s Guide

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Revision History

September 2010 Online only New for Version 3.0 (Release 2010b)

Page 3

Simulating Sensitivity Measurements

Example — Modeling System Noise Figure ........... 1-2

Creating a Low-IF Receiver Model Simulating a Thermal Noise Floor Computing System Noise Figure

.................... 1-2

.................... 1-6

..................... 1-7

Contents

Designing a Receiver with an ADC

Example — Overcoming Quantization Error of an ADC Measuring the Quantization Noise Floor Improving Receiver-ADC Performance

.................. 1-9

.............. 1-12

................ 1-13

Simulating RF Interference

Example — Carrier to Interference Performance of a

Weaver Receiver

Creating a Model with RF Interference Modeling RF and Blocker Sources Simulating LO Phase Offset

Modeling LO Phase Noise

Creating a Model with Phase Noise Shaping the LO Noise S kirt

................................ 2-2

................ 2-2

.................... 2-7

......................... 2-7

.......................... 2-8

................... 2-8

......................... 2-11

.. 1-9

Simulating Intermodulation Distortion

Example — Modeling a Direct Conversion Receiver ... 3-2

iii

Page 4

Creating a Direct Conversion Receiver Model ........... 3-2

Modeling System-Level Components Examining DC Impairments

........................ 3-7

.................. 3-6

iv Contents

Page 5

Simulating Sensitivity Measurements

• “Example — Modeling System Noise Figure” on page 1-2

• “Designing a Receiver with an ADC” on page 1-9

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1 Simulating Sensitivity Measurements

Example — Modeling System Noise Figure

RF receivers amplify signals and translate them to lower frequencies. The receiver itself introduces noise that degrades the received signal. The signal-to-noise ratio (S NR) at the receiver output ultimately determines the usability of the receiver.

1-2

The preceding figure illustrates the effect of the receiver on the signal. The receiver amplifies a low-power RF signal at the carrier f and downconverts the sig n al to f determines the difference between the SNR at the output and the SNR at the input:

SNR SNR NF

where the difference is calculated in decibels. Excessive noise figure in thesystemcausesthenoisetooverwhelmthesignal,makingthesignal unrecoverable.

=−

out in sys

. The noise figure (NF) of the system

with a high SNR

Creating a Low-IF Receiver Model

The model

_simrf_snr

Page 7

Example — Modeling System Noise Figure

simulates a simplified IF receiver architecture. A Sinusoid block and a Noise block model a two-tone input centered at f RF system amplifies the signal and mixes it with the local oscillator f to an intermediate frequency f

. A voltage sensor recovers the signal at the IF.

and low-level thermal noise. The

down

The amplifier contributes 40 dB of gain and a 15-dB noise figure, and the mixer contributes 0 dB of gain and a 20-dB noise figure, which are values characteristic of a relatively noisy, high-gain receiver. The two-tone input has aspecifiedlevelof.1μV. A 1-V level in the local oscillator ensures consistency with the formulation of the conversion gain of the mixer.

To run the model:

1 Open the model by clicking the link or by typing the model name at the

Command Window prompt.

2 Select Simulation > Start.

Models that contain SimRF™ Amplifier, Mixer, or S-Parameter blocks generate files in the current MATLAB

directory at runtime. However, you can configure the output location for these files by specifying a cache folder in the Simulink Preferences dialog box. To specify a cache folder, open the Simulink Preferences dialog box (File > Preferences) and specify a location

1-3

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1 Simulating Sensitivity Measurements

on your file system for the Simulink cache folder parameter. For more information about the Simulink

interface, see Simulink Preferences Window.

Setting Up the SimRF Environment

The model simulates according to the following settings:

• In the SimRF Parameters Block Parameters dialog box, the Carrier

Frequencies parameter specifies the carriers o f the SimRF environment:

- f

, the carrier of the desired signal, equal to 2 G Hz .

- f

, the frequency of the LO in the first mixing stage, equal to

1.9999 GHz.

- f

, the intermediate frequency, equal to fRF– fLO, or 100 kHz.

This example uses the variable function, to specify the carriers.

• In the Solver Configuration Block Parameters dialog box, the Use local

solver box is selected. This setting causes the SimRF environment to

simulate with a local solver with the following settings:

car_env, defined in the initialization

- The Solver type is set to Trapezoidal rule.

- The Sample time parameter is set to 1/64.

Since the model uses a local solver, the global solver settings do not affect the simulation within the SimRF environment. For more information on global and local solvers, see Choosing Simulink and Simscape™ Solvers.

1-4

Viewing Simulation Output

The model uses subsystems with an Embedded M A TLAB®implementation of a fast Fourier transform (FFT) to generate two plots. The FFT uses 64 bins, so for a sampling frequency of 64 Hz, the bandwidth of each bin is 1 Hz. Subsequently, the power levels shown in the figures also represent the power spectral density (PSD) of the signals in dBm/Hz.

• The Input Display plot shows the power spectrum of the signal and noise

at the input of the receiver.

Page 9

Example — Modeling System Noise Figure

The measured p ow er of each tone is consistent with the expected power level of a .1-μV two-tone envelope:

⎛

⎞

log

⎜ ⎜ ⎝

⎛ ⎜ ⎜⎜ ⎜ ⎜ ⎜ ⎜

⎝

⎛

1210

⎜ ⎜

⎝

⎟ ⎟ ⎠

−

⋅

250

⎞

⎟

⎟ ⎟

⎟

⎠

⎟

+=−30 142 dBm

⎟ ⎟ ⎟

⎠

Afactorof1/2isduetovoltagedivision across source and load resistors, and another factor of 1/2 is due to envelope scaling. See the demo Two-Tone Envelope Analysis Using Real Signals f or more discussion on scaling envelope signals for power calculation.

The measured noise floor at -177 dBm/Hz is reduced by 3 dB from the specified -174 dBm/Hz noise floor. The difference is due to power transfer from the source to the input of the amplifier.

• The Output Display plot shows the power spectrum of the signal and noise

at the output of the receiver.

1-5

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1 Simulating Sensitivity Measurements

The measured PSD of -102 dBm/Hz for each tone is consistent with the 40-dB combined gain of the amplifier and mixer. The noise PSD in the figureisshowntobeapproximately50dBhigherattheoutput,duetothe gain and noise figure of the system.

1-6

If you have Signal Processing Blockset™ software installed, you can replace the Embedded MATLAB subsystems with Vector Scope or Spectrum Scope blocks.

Simulating a Thermal Noise Floor

The model uses a block to model a thermal noise floor according to the equation

PkTRf

= 4 Δ

noise B s

where:

• k

is Boltzmann’s constant, equal to 1.38065 × 1023J/K.

• T is the noise temperature, specified as 293 K in this example.

is the noise source impedance, specified as 50 Ω inthisexampletoagree

• R

with the resistance value of the Resistor block labeled ’Source Resistor’.

• Δf is the noise bandwidth.

Page 11

Example — Modeling System Noise Figure

To model the noise floor, the model uses a combination of settings in two different blocks.

• In the Noise block dialog box, the Noise P ower Spectral Density

(Watts/Hz) parameter is set to the variable

noise_level,whichis

calculated in the initialization function to equal the value of the expression

PfkTR

/ Δ=4

noise B s

• In the SimRF Parameters block dialog box:

- The Sim ulate Noise box is selected. When this box is cleared, the

model simulates without noise.

- The Noise bandwidth type parameter is set to Absolute bandwidth.

- The Noise bandwid th is 1/sample_time,wheresample_time is the

discrete sample time used by the local solver. This setting matches the Sample time parameter in the Solver Configuration dialog box. This value specifies Δf in the preceding expressions.

Computing System Noise Figure

To model RF noise from component noise figures:

1 Select Simulate noise in the SimRF Parameters block dialog box, if it is

not already selected.

2 Specify a value for the Noise figure (dB) parameter of an Amplifier and

Mixer blocks.

The noise figures are not strictly additive. The amplifier contributes more noise to the system than the mixer because it appears first in the cascade. To calculate the total noise figure of the RF system with n stages, use the Friis equation:

=+−+

sys

−

...

12 12 1

...

GG G

−

where Fiand Giarethenoisefactorandgainoftheith stage, and NF

=10log10(Fi).

1-7

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1 Simulating Sensitivity Measurements

⎝

⎠

In this example, the noise figure of the amplifier is 10 dB, and the noise figure ofthemixeris15dB,sothenoisefigureofthesystemis:

10 10

log .

The Friis equation shows that although the mixer has a higher noise figure, the amplifier contributes more noise to the system.

For more information on RF system noise figure, see the demo Impact of RF Receiver on Communcations System Performance.

15 10

⎛

10 10

⎜ ⎜

10 1

⎞

− ⎟

⎟

= dB

10 3

1-8

Page 13

Designing a Receiver with an ADC

Most RF receivers in modern communications or radar systems feed signals to an analog-to-digital converter (ADC). Due to their finite resolution, A DCs introduce quantization error into the system. The resolution of the ADC is determined by the number of bits and the full-scale (FS) range of the ADC.

Designing a Receiver with an ADC

The preceding fi gure illustrates an RF signal that falls within the dynamic range (DR) of an ADC. The input signal and noise at the carrier f signal-to-noise ratio (SNR). The received signal at f to system noise figure. However, if thequantizationerrorisnearorabove the receiver noise, system performance degrades.

ToensurethattheADCcontributesnomorethan0.1dBofnoisetothesignal at f

, the quantization noise floor must be 16 dB lower than the receiver

noise. Thi s condition can be met by:

• Reducing the full-scale range or increasing the resolution of the ADC,

which lowers the quantization noise floor.

• .Increasing the gain of the RF receiver, which raises the receiver noise floor.

has reduced SNR due

has high

Example — Overcoming Quantization Error of an ADC

The model

1-9

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1 Simulating Sensitivity Measurements

ex_simrf_adc

simulates a low-IF receiver with an ADC. This model is based on the model

ex_simrf_snr described in the se ction “Creating a Low-IF Receiver Model” on

page 1-2. At the output of the RF system, the ADC subsystem models an ADC with an FS range of

sqrt(100e-3) V and a resolution of 16 bits.

1-10

The power a voltage signal a

10 100 30 0

log

−

+=dBm

t the full-scale range of the ADC is

To run the model:

1 Open the model by clickin

g the link or by typing the model name at the

Command Window prompt.

2 Select Simulation > Start.

Viewing Simulation Output

The model uses subsystems with an Embedded MATLAB implementation of a fast Fourier transform (FFT) to generate two plots. The FFT uses 64 bins, so for a sampling frequency of 64 Hz, the bandwidth of each bin is 1 Hz. Subsequently, the power levels shown in the figures also represent the power spectral density (PSD) of the signals in dBm/Hz.

Page 15

Designing a Receiver with an ADC

• The Input Display plot shows the power spectrum of the two-tone signal

and noise at the input of the receiver-ADC system.

The measured power o f each tone of -142 dBm is consistent with the expected power level of a .1-μV signal. The power level of the noise is consistent with a -174 dBm/Hz noise floor.

• The Output Display plot shows power spectrum of the output signal.

1-11

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1 Simulating Sensitivity Measurements

The quantization error exceeds the receiver noise.

If you have Signal Processing Blockset software installed, you can replace the Embedded MATLAB subsystems with Vector Scope or Spectrum Scope blocks.

1-12

Measuring the Quantization Noise Floor

To calculate the quantization noise floor of the ADC, subtract the dynamic range from the full-scale power, which is 0 dBm. To calculate the dynamic range PSD for the ADC, use the equation:

DR N f

where

• N

bits

• Δf is the bandwidth of the FFT, which is 64 in this example. Oversampling

in an ADC yields lower quantization noise.

• The value 1.76 is a correction factor for a pure sinusoidal input.

Therefore, the quantization noise floor is -116 dBm/Hz, in agreement w i th the measured output levels.

=⋅

ADC bits

is the resolution. The ADC in this example uses 16 bits.

.log..Δ dBm/Hz

+=+6 02 10 1 76 116 1

()

Page 17

Designing a Receiver with an ADC

Improving Receiver-ADC Performance

Increasing the gain in the mixer raises the receiver noise without increasing the noise figure. Calculate the mixer gain required to achieve a 16-dB margin between the quantization noise floor and the receiver noise:

GQNF GNF

=+−−++

mixer ADC sys sys

()( )

=− + −− + +

(. )(

116 1 16 174 40 110 3

100 1 123 7

=− + = dB

23 6

16 174

To simulate a receiver that cle ars the quantization noise floor:

1 Set the Available power gain parameter of the mixer to 23.6.

2 Select Simulation > Start.

The figure shows that the receiver noise is 16 dB above the quantization noise floor. Therefore, the SNR at the output is dominated by the receiver noise.

1-13

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1 Simulating Sensitivity Measurements

1-14

Page 19

Simulating RF Interference

• “Example — Carrier to Interference P erformance of a Weaver Receiver”

on page 2-2

• “Modeling LO Phase Noise” on page 2-8

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2 Simulating RF Interference

Example — Carrier to Interference Performance of a Weaver Receiver

A classic superhetorodyne architecturefiltersimagespriortofrequency conversion. In contrast, image-reject receivers remove the images at the output without filtering but are sensitive to phase offsets.

The preceding figure illustrates two input signals a t the ca rriers fRFand

that both differ from the LO frequency, f

translates both input signals down to f

IF1

stage of the receiver removes the image signal from the output entirely.

,byanamountf

LO1

. Perfect image r ej ection in the final

. Mixing

IF1

2-2

Creating a Model with RF Interference

The model

ex_simrf_ir

simulates image rejection in a Weaver architecture. The receiver downconverts the signals at f

and fIMto f

IF1

and f

in two sequential stages.

IF2

Page 21

To run the model:

Example — Carrier to Interference Performance of a Weaver Receiver

1 Open the model by clicking the link or by typing the model name at the

Command Window prompt.

2 Select Simulation > Start.

Models that contain SimRF Amplifier, M ixer, or S-Parameter blocks generate files in the current MATLAB directory at runtime. However, you can configure the output location for these files by specifying a cache folder in the Simulink Preferences dialog box. To specify a cache folder, open the Simulink Preferences dialog box (File > Preferences) and specify a location on your file system for the Simulink cache folder parameter. For more information about the Simulink interface, see Simulink Preferences Window.

Setting Up the SimRF Environment

The model runs according to the following settings:

2-3

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2 Simulating RF Interference

• In the SimRF Parameters Block Parameters dialog box, the Carrier

Frequencies parameter specifies the carriers o f the SimRF environment:

- f

, the RF carrier.

- f

, the image carrier.

- f

, the frequency of the LO in the first mixing stage.

LO1

- f

, the frequency of the LO in the second m ixing stage.

LO2

- f

, the intermediate frequency of the signal after the first mixing stage,

IF1

equal to f

- f

, the intermediate frequency of the signal after the second mixing

IF2

stage, equal to f

• In the Solver Configuration Block Parameters dialog box, the Use local

solver box is selected. This setting causes the SimRF environment to

simulate with a local solver with the following settings:

– fRFand fIM– f

LO1

– fIM.

LO2

LO1

- Solver type is Trapezoidal rule.

- Sample time is below the Nyquist frequency of the modulation.

2-4

Viewing Simulation Output

The model uses subsystems with an Embedded MATLAB implementation of a fast Fourier transform (FFT) to generate four plots.

• The RF D isplay plot shows the power spectrum of the signal recovered from

the carrier f parameter of the preceding SimRF Outport block.

,specifiedascarriers.RF in the Carrier Frequencies

Page 23

Example — Carrier to Interference Performance of a Weaver Receiver

The modulation of the RF carrier is a constant envelope generated by a Continuous Wave block which generates a single peak centered at the carrier.

• The Image Display plot shows the power spectrum of the image. The signal

is recovered from the carrier f

,specifiedascarriers. IM in the Carrier

Frequencies parameter of the preceding SimRF Outport block.

2-5

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2 Simulating RF Interference

The Sinusoid source generates a two-tone signal centered at fIM.

• The IF1 Display plot shows a power spectrum centered at the first

intermediate frequency, measured between the first and second stages. Thesensoroutputsthemodulation from the carrier f

carriers.IF2 in the Carrier Frequencies parameter of the preceding

,specifiedas

IF1

SimRF Outport block.

2-6

Both the RF and image appear on the carrier. The power level of the image 40 dB higher than the RF.

• The Output Display plot shows the effects of the RF system. The sensor

outputs the modulation from the carrier f

,specifiedascarriers.IF1 in

IF2

the Carrier Frequencies para m eter of the preceding Sim RF Outport block.

Page 25

Example — Carrier to Interference Performance of a Weaver Receiver

As expected, the system removes the image and amplifies the RF by 6 dB.

If you have Signal Processing Blockset software installed, you can replace the Embedded MATLAB subsystems with Vector Scope or Spectrum Scope blocks.

Modeling RF and Blocker Sources

To model more robust input signals, you can use a SimRF Inport block to specify a circuit envelope generated using blocks from other Simulink libraries. For example, the demo Impact of RF Receiver on Communications System Performance uses Communications Blockset™ blocks to model a QPSK-modulated waveform of random bits with SimRF Inport that brings the signal into the SimRF environment.

Simulating LO Phase Offset

The phase shifters have specified Phase shift parameters of 90.Deviation from this value results in a phase offset and causes imperfect image rejection. The demo Simulating Image Rejection Ratio Measurements analyzes the IRR of the Weaver and Hartley architectures several times, calculating the image rejection ratio (IRR) for several d ifferent phase offsets.

2-7

Page 26

2 Simulating RF Interference

Modeling LO Phase Noise

A mixer transfers local oscillator (LO) phase noise directly to its output.

The preceding figure shows the transfer of phase noise from f

LO1

to f

IF1

Creating a Model with Phase Noise

The model

ex_simrf_phase_noise

introduces phase noise into the model from the section “Creating a Model with RF Interference” on page 2-2. The first mixing stage downconverts the RF and image to f

2-8

Page 27

Modeling LO Phase Noise

Viewing Simulation Output

The model uses subsystems with an Embedded MATLAB implementation of a fast Fourier transform (FFT) to generate four plots.

• The IF1 Display plot shows a power spectrum centered at the first

intermediate frequency, measured between the first and second stages.

2-9

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2 Simulating RF Interference

The figure shows that the LO phase noise has been transferred to the image. The RF signal on the carrier f its power level is below the phase noise pow er of the downconverted image signal. ThetwovisiblepeaksareatthesamepowerastheIFshowninthe previous section, “Creating a Model with RF Interference” on page 2-2.

is not visible in the f igure because

IF1

2-10

• The Output Display plot shows the downconverted RF with the images

removed.

Page 29

Modeling LO Phase Noise

The LO phase noise has been transferred to the receiver output. The peak signal power is the same as in the previous section, “Creating a Model with RF Interference” on page 2-2.

If you have Signal Processing Blockset software installed, you can replace the Embedded MATLAB subsystems with Vector Scope or Spectrum Scope blocks.

Shaping the LO Noise Skirt

To simulate phase noise, the model phase modulates p ink noise generated in the LO with Phase Noise subsystem:

The subsystem contains the following blocks:

• A Random Number block outputs a Gaussian random number at discrete

time steps to generate white noise.

• A Gain block scales the signal by a factor of

210



where f

rel

is the LO frequency and P

LO1

is the relative noise power density

rel

in dBc/Hz.

• A Discrete Filter block filters the uniform white noise to generate 1/f noise.

• A Magnitude-Angle to Complex block phase modulates an input signal

The output is of the form exp(j

• A SimRF Inport block models a controlled voltage source in the SimRF

environment, modulating the carrier f circuit-envelope equivalent signal is exp[j(

with the input signal exp(jϕ). The

2πf

t +ϕ(t))].

LO1

2-11

Page 30

2 Simulating RF Interference

If you have Communications Blockset software installed, use the Phase Noise block to add phase noise to a given input signal.

2-12

Page 31

Simulating Intermodulation Distortion

Page 32

3 Simulating Intermodulation Distortion

Example — Modeling a Direct Conversion Receiver

In this section...

“Creating a Direct Conversion Receiver Model” on page 3-2

“Modeling System-Level Components” on page 3-6

“Examining DC Impairments” on page 3-7

Direct-conversion receivers are sensitive to second-order intermodulation products because they transfer the RF signal directly to baseband.

Creating a Direct Conversion Receiver Model

The model

ex_simrf_dc

models a direct-conversion receiver within the SimRF environment. The RF system consists of a low-noise amplification (LNA) stage, a direct-conversion stage, and a final amplification stage. The receiver specifications are similar to the specifications used in the Design and Simulation of a Direct Conversion Receiver demo, which elaborates on the impairments shown in this example.

3-2

Page 33

Example — Modeling a Direct Conversion Receiver

To run the model:

1 Open the model by clicking the link or by typing the model name at the

Command Window prompt.

2 Select Simulation > Start.

Setting Up the SimRF Environment

The model runs according to the fo ll owing environment se tti ngs:

• In the SimRF Parameters Block Parameters dialog box, the Carrier

Frequencies parameter specifies the carriers in the SimRF environment:

- f

= fLO, the carrier of the RF and the local oscillator.

- f

, the blocker carrier

The SimRF environment always simulates the 0 Hz carrier, reg ardless of whether the SimRF Parameters block specifies it.

• In the Solver Configuration Block Parameters dialog box, the Use local

solver box is selected. This setting causes the SimRF environment to

simulate with a local solver with the following settings:

- Solver type is Trapezoidal rule.

- Sample time is sample_time, defined as 1.25e-4 in the model

initialization function. Since the model uses a local solver, the global solver settings do not affect the simulation within the SimRF environment. For more information on global and local solvers, see Choosing Simulink and Simscape Solvers.

3-3

Page 34

3 Simulating Intermodulation Distortion

Viewing Simulation Output

The model uses subsystems with an Embedded MATLAB implementation of a fast Fourier transform (FFT) to generate four plots:

• The RF Display plot shows the power level of the RF signal.

3-4

The power level of the RF is about 100 dBm.

• The Blocker Display p lot shows the power spectrum centered at the carrier

Page 35

Example — Modeling a Direct Conversion Receiver

The power level of the blocker is about 90 dB higher than the signal power of the RF..

• The In-Phase Output plot shows the power spectrum of the in-phase signal

at baseband.

In the figure, DC power is a direct result of the blocker and the IP2 in the mixers.

3-5

Page 36

3 Simulating Intermodulation Distortion

• The Quadrature Output plot shows the power spectrum of the quadrature

signal at baseband.

The quadrature output only contains noise because the input signal and blocker have no quadrature components.

3-6

If you have Signal Processing Blockset software installed, you can replace the Embedded MATLAB subsystems with Vector Scope or Spectrum Scope blocks.

Modeling System-Level Components

The IP2 and IP3 parameters specify the second- and third-order intercept points of Amplifier and Mixer blocks:

• The amplifiers have infinite IP2 and IP3, so the amplifiers are li n ear.

• IP2 of the mixer is

Amplifier and Mixer components have specified gains and noise figures:

• The gain and noise figure in the LNA stage are 25 dB and 6 dB, respectively.

• The gain and noise figure in the mixing stage are 10 dB and 10 dB.

The Input impedance (ohms) parameters of the two mixers are both

-10 dB

Page 37

Example — Modeling a Direct Conversion Receiver

100, which sum in parallel to a resistance of 50 Ω to match the output

impedance of the LNA.

• The gain and noise figure in the final amplification stage are 20 dB and

15 dB, respectively.

To calculate RF system noise figure, use the Friis equation:

=+−+

sys

−

...

12 12 1

GG G

...

−

where Fiand Giare the noise factor and gain of the ith stage. For more information on RF system noise figure, see the demo Impact of RF Receive r on Communcations System Performance.

Examining DC Impairments

In addition to intermodulation distortion from IP2, direct-conversion receivers are subject to additional DC impairments. For example, couplin g between mixer input and local oscillator (LO) ports causes self-mixing of the LO. For more information, see the demo Executable Specification of a Direct Conversion Receiver.

3-7

Matlab SIMRF 3 user guide

Specifications and Main Features

Frequently Asked Questions

User Manual