Superheterodyne Receiver RF Front End (Amps, Filters) Local Oscillator Mixer IF Strip (Amps, Filters) Channel SelectivityService Band Detector (Demodulation) Multiplication in the Time Domain = Convolution (shifting) in the Frequency Domain Recovered Information

Image Effect 11 22 33  3  2  1  1  2  1  2  1  2  1  2  3  2  3  2  3  2  3  2 Local Oscillator  3  2 =  2  1

Image Effect (cont) BW IF f IF f LO f LO + f IF f LO - f IF Upper Conversion Band Lower Conversion Band Desired Channel Image Band Low Side Injection High Side Injection Any signals entering the mixer in the Desired Channel and/or the Image Band will be converted down into the IF bandwidth, amplified, and demodulated. This includes: 1.Desired and interfering (image band) signals entering the antenna 2.kTB noise amplified by the RF amplifiers

Observations The desired channel and its image band are always separated by twice the IF frequency.. The LO frequency is always exactly between the desired channel and its image band, fLOfLO f LO + f IF f LO - f IF Upper Conversion Band Lower Conversion Band

Observations (cont) The higher the IF frequency, the greater the frequency displacement between the desired channel and its image band. f IF fLOfLO f LO + f IF f LO - f IF

Observations (cont) Filtering (pre-selector) before the mixer, in the RF front end, can reduce the effects of image band signals and kTB noise. LO DS US Service Band Range Image Band Range LO Range Pre-selector Response Image Rejection for DS Worst Case Image Rejection

Pre-selector Math Image Rejection for DS Worst Case Image Rejection f c : Center of Service Band and Pre-selector pass-band BW S : Pre-selector Passband ~ Service Band Range Image Rejection Shape factor for Specific Channel DS: Worst Case Image Rejection Shape Factor f s,MAX DS US 2f IF (Low-side Injection) (High-side Injection) US DS 2f IF f s,MIN

Image Band Thermal Noise A pre-selector filter between the antenna and first RF amp limits all out of band interfering signals entering the receiver, including images But does not reduce thermal noise in the image band. Absent additional mitigation, this will allow thermal noise power equal to kT 0 B from both the image band and desired channel to enter the mixer and pass through the IF. This effectively doubles the noise bandwidth, and the effective noise power entering the receiver is 2kT 0 B, where B is the IF bandwidth. If a second pre-selector is included following the first RF amplifier, the amplified thermal noise in the image band can be reduced to well below the amplified on-channel thermal noise (which we can’t do anything about), effectively eliminating it, as well as providing additional image rejection. Pre-selector RF Amp Pre-selector RF Amp Mixer

Effect on Noise Figure When determining the noise figure/ratio of the receiver, structure and the placement of the pre-selector filters must be taken into consideration. If a pre-selector is included between the first RF amp and the mixer, there is no appreciable noise power contribution from the image band, and Friis’ formula will provide an accurate noise ratio. If there is no pre-selector between the first RF amp and the mixer, then the result of Friis’ formula must be doubled (add 3 dB to resultant noise figure) to account for the excess noise contribution from the image band.

Computing Image Rejection 1.Determine the shape factors for the desired frequency and image frequency (mid-band or band edge) for all pre-selectors (they may have different bandwidths). 2.Based on the poles/ripple of each pre-selector, determine the attenuations corresponding to the shape factors determined in step 1. 3.The image rejection for each filter is the difference between the attenuation for the image and the attenuation for the desired frequency. 4.The total image rejection in dB is the sum of the image rejections in dB as determined in step 3.

Pre-selector A RF Amp Pre-selector B RF Amp Mixer Example Pre-selector A: fc = 121 Mhz, BW 3dB =8 Mhz 2 Poles, 0 dB ripple Pre-selector B: fc = 121 Mhz, BW 3dB = 7.5 Mhz 3 Poles, 0.1 dB ripple Q U = 80 Service Band: 118 – 124 Mhz IF: 9.4 Mhz, Low Side Injection DS: 124 Mhz US: Mhz Worst Case Image Rejection f c : 121 Mhz BW S : 6 MhzImage Band BW 3dB 18.8 Mhz

Worst case Image Frequency: 124Mhz – 2(9.4 Mhz) = Mhz (FM Broadcast) Preselector 124 Mhz 124 Mhz Mhz Mhz IRR(dB)Ins Loss (Midband) Ins 124 Mhz A B Total Worst Case Image Rejection Ratio = 66.5 dB