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Multiplication in the Time Domain = Convolution (shifting) in the Frequency Domain. Superheterodyne Receiver. Mixer. RF Front End (Amps, Filters). IF Strip (Amps, Filters). Detector (Demodulation). Recovered Information. Service Band. Channel Selectivity. Local Oscillator. -w 1. w 1.

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superheterodyne receiver

Multiplication in the Time Domain = Convolution (shifting) in the Frequency Domain

Superheterodyne Receiver

Mixer

RF Front End

(Amps, Filters)

IF Strip

(Amps, Filters)

Detector

(Demodulation)

Recovered Information

Service Band

Channel Selectivity

Local Oscillator

image effect

-w1

w1

Image Effect

w3-w2 = w2-w1

Local Oscillator

-w2

w2

-w3

w3

-w1-w2

w1-w2

-w1+w2

w1+w2

-w3-w2

-w3+w2

w3-w2

+w3+w2

image effect cont
Image Effect (cont)

Upper Conversion Band

Lower Conversion Band

Image Band

Image Band

Desired Channel

Desired Channel

BWIF

fLO + fIF

fIF

fLO - fIF

fLO

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.

Low Side Injection

High Side Injection

  • This includes:
    • Desired and interfering (image band) signals entering the antenna
    • kTB noise amplified by the RF amplifiers
observations
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,

Upper Conversion Band

Lower Conversion Band

fLO + fIF

fLO - fIF

fLO

observations cont
Observations (cont)

The higher the IF frequency, the greater the frequency displacement between the desired channel and its image band.

fLO + fIF

fIF

fLO - fIF

fLO

observations cont1
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 Range

Pre-selector Response

DS

LO

US

Worst Case Image Rejection

Image Rejection for DS

Image Band Range

Service Band Range

pre selector math
Pre-selector Math

BWS :

Pre-selector Passband

~ Service Band Range

2fIF

2fIF

fs,MIN

fs,MAX

US

DS

DS

US

Image Rejection for DS

Worst Case Image Rejection

fc : Center of Service Band and Pre-selector pass-band

Image Rejection Shape factor for Specific Channel DS:

Worst Case Image Rejection Shape Factor

(Low-side Injection)

(High-side Injection)

image band thermal noise
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 kT0B 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 2kT0B, 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.

Mixer

RF Amp

RF Amp

Pre-selector

Pre-selector

effect on noise figure
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
Computing Image Rejection

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).

Based on the poles/ripple of each pre-selector, determine the attenuations corresponding to the shape factors determined in step 1.

The image rejection for each filter is the difference between the attenuation for the image and the attenuation for the desired frequency.

The total image rejection in dB is the sum of the image rejections in dB as determined in step 3.

slide11

Example

Service Band: 118 – 124 Mhz

IF: 9.4 Mhz, Low Side Injection

Mixer

RF Amp

RF Amp

Pre-selector

A

Pre-selector

B

Pre-selector A: fc = 121 Mhz, BW3dB =8 Mhz 2 Poles, 0 dB ripple

Pre-selector B: fc = 121 Mhz, BW3dB = 7.5 Mhz 3 Poles, 0.1 dB ripple

QU = 80

BW3dB

Image Band

BWS : 6 Mhz

18.8

Mhz

DS:

124 Mhz

US:

105.3 Mhz

Worst Case Image Rejection

fc : 121 Mhz

slide12

Worst case Image Frequency: 124Mhz – 2(9.4 Mhz) = 105.3 Mhz (FM Broadcast)

Total Worst Case Image Rejection Ratio = 66.5 dB