A classic superheterodyne architecture filters images prior to frequency 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 at the carriers fRF and fIM that both differ from the LO frequency, fLO1, by an amount fIF1. Mixing translates both input signals down to fIF1. Perfect image rejection in the final stage of the receiver removes the image signal from the output entirely.
The model ex_simrf_ir simulates image rejection in a Weaver architecture. The receiver downconverts the signals at fRF and fIM to fIF1 and fIF2 in two sequential stages.
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Select Simulation > Run.
To maximize performance, the Fundamental tones and Harmonic order parameters specify the minimal set of simulation frequencies explicitly in the Configuration block:
fRF, the RF carrier, equals 100 MHz.
fLO1, the frequency of the LO in the first mixing stage, equals 150 MHz
fIM, the image of the RF carrier relative to fLO1, equals 200 MHz.
fIF1, the intermediate frequency of the signal after the first mixing stage, equals fLO1 – fRF = fIM – fLO1 = 50 MHz.
fLO2, the frequency of the LO in the second mixing stage, equals 75 MHz.
fIF2, the intermediate frequency of the signal after the second mixing stage, equals fLO2 – fIF1 = 25 MHz. In this system, every carrier is a multiple of fIF2. The largest carrier, fIM, is the 8th harmonic of fIF2, so setting Fundamental tones to fIF2 and Harmonic order to 8 ensures that every carrier is in the set of simulation frequencies.
Solver conditions and noise settings are also specified for the Configuration block:
The Solver type is set to auto. For more information on choosing solvers, see the reference page for the Configuration block or see Choosing Simulink® and Simscape™ Solvers.
The Sample time parameter is set to 1/(mod_freq*64). This setting ensures a simulation bandwidth 64 times greater than the envelope signals in the system.
The Simulate noise box is checked, so the environment includes noise parameters during simulation.
The model uses subsystems with a MATLAB Coder™ implementation of a fast Fourier transform (FFT) to generate four plots.
The RF Display plot shows the power spectrum of the signal recovered from the carrier fRF, specified as carriers.RF in the Carrier frequencies parameter of the preceding SimRF Outport block.
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 fIM, specified as carriers.IM in the Carrier frequencies parameter of the preceding SimRF Outport block.
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. The sensor outputs the modulation from the carrier fIF1, specified as carriers.IF2 in the Carrier frequencies parameter of the preceding SimRF Outport block.
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 fIF2, specified as carriers.IF1 in the Carrier frequencies parameter of the preceding SimRF Outport block.
As expected, the system removes the image and amplifies the RF by 6 dB.
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 featured example Impact of an RF Receiver on Communication System Performance uses Communications System Toolbox™ blocks to model a QPSK-modulated waveform of random bits with SimRF Inport that brings the signal into the SimRF™ environment.
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 featured example Measuring Image Rejection Ratio in Receivers analyzes the IRR of the Weaver and Hartley architectures several times, calculating the image rejection ratio (IRR) for several different phase offsets.