Image Frequency Rejection

In a superheterodyne receiver, the image frequency is an unwanted frequency that, when mixed with the local oscillator, produces the same intermediate frequency as the desired signal. If the image is not suppressed before the mixer, it causes co-channel interference that is completely indistinguishable at the IF stage. Image frequency rejection is therefore a fundamental requirement of receiver front-end design.

Why Image Frequency Arises

When the mixer multiplies the incoming RF signal at fs with the local oscillator at fLO, the output contains spectral components at both fLO + fs and fLO - fs. The IF bandpass filter selects the component at fIF = fLO - fs. However, any input signal at a frequency fimage where fimage - fLO also equals fIF (considering absolute value) will similarly produce an output at fIF after mixing. This is the image signal.

For high-side injection where fLO = fs + fIF, the image frequency falls at fimage = fLO + fIF = fs + 2*fIF. For low-side injection where fLO = fs - fIF, the image falls at fimage = fLO - fIF = fs - 2*fIF. The separation between the desired signal and its image is always exactly 2*fIF, regardless of which station is tuned. This is the crucial relationship because it tells us that a higher IF places the image further away, making it easier to reject with the RF filter.

The image rejection ratio (IRR) quantifies how well the receiver suppresses the image frequency relative to the desired signal. It is defined as the ratio of the receiver's response at the desired frequency to its response at the image frequency, expressed in dB. A well-designed receiver should achieve at least 40 dB of image rejection; professional receivers often achieve 60 to 80 dB.

Role of the RF Filter (Preselector)

The RF preselector filter is a tunable bandpass filter placed between the antenna and the mixer. Its sole purpose is to pass the desired signal frequency and attenuate the image frequency before it reaches the mixer. Since the image frequency is 2*fIF away from the desired frequency, the preselector must provide sufficient attenuation at that offset.

The effectiveness of the preselector is directly related to its Q factor and the IF chosen. If fIF is large, the image is 2*fIF away from the signal and even a moderate Q preselector can provide adequate rejection. If fIF is small, the image is close to the signal and the preselector must have very high Q and sharp roll-off to reject it. This creates the classical design trade-off between image rejection and IF selectivity.

In modern integrated receivers, especially those operating at microwave frequencies, the preselector may be a simple low-pass or bandpass filter that is not tunable. In such cases, the choice of IF becomes even more critical, and sometimes a double conversion architecture is used to achieve both good image rejection and good IF selectivity simultaneously.

Mathematical Expression for Image Rejection

For a single-tuned RF preselector with quality factor Q tuned to the signal frequency fs, the voltage attenuation at a frequency f is approximately given by the normalized selectivity function. The image rejection at fimage = fs + 2*fIF is approximately:

IRR (in linear) = sqrt(1 + (Q * (fimage/fs - fs/fimage))^2). For fimage much larger than fs, this simplifies to approximately Q * 2*fIF / fs. This shows that image rejection improves with higher Q, higher fIF, and lower signal frequency.

Given:
FM broadcast receiver
Desired station fs = 98 MHz
IF fIF = 10.7 MHz (standard FM IF)
High-side injection
RF preselector Q = 50

Why this formula applies:
Image frequency is at fs + 2*fIF for high-side injection
IRR_linear = sqrt(1 + (Q*(fimg/fs - fs/fimg))^2)

Formula:
fLO = fs + fIF
fimage = fs + 2*fIF
Let x = fimg/fs - fs/fimg
IRR_linear = sqrt(1 + (Q*x)^2)
IRR_dB = 20*log10(IRR_linear)

Substitution:
fLO = 98 + 10.7 = 108.7 MHz
fimage = 98 + 2*10.7 = 119.4 MHz
x = (119.4/98) - (98/119.4) = 1.2184 - 0.8207 = 0.3977
Q*x = 50 * 0.3977 = 19.885
IRR_linear = sqrt(1 + 19.885^2) = sqrt(1 + 395.4) = sqrt(396.4) = 19.91

Calculation:
IRR_dB = 20 * log10(19.91) = 20 * 1.299 = 25.97 dB

Final Answer: Image rejection ratio = approximately 26 dB for Q=50 RF preselector. This is marginal for a practical receiver (typically 40+ dB required), indicating that the FM broadcast standard's choice of 10.7 MHz IF was designed to rely on a moderate-Q preselector for adequate image rejection.

Exam Tip: Image frequency = fs + 2*fIF (high-side injection). The separation between signal and image is always 2*fIF. Higher IF improves image rejection but worsens IF selectivity. The RF preselector (not the IF filter) provides image rejection. These are two separate filtering functions with two different design requirements.

• Image frequency arises from the mixing process: any signal at fimage that produces the same IF as the desired signal is an image. For high-side injection, fimage = fs + 2*fIF.
• The RF preselector filter provides image rejection before the mixer. The IF filter cannot reject the image because the image arrives at the IF output at the same frequency as the desired signal.
• Image rejection improves with higher IF (image moves further from signal) and higher preselector Q (steeper filter roll-off).
• IRR in dB = 20*log10(sqrt(1 + (Q*(fimg/fs - fs/fimg))^2)). Practical receivers need minimum 40 dB IRR.
• Standard IF choices (455 kHz for AM, 10.7 MHz for FM) represent the optimized trade-off between image rejection and IF selectivity for those respective applications.

Quick Revision

• Image frequency: fimage = fs + 2*fIF (high-side), fimage = fs - 2*fIF (low-side). Separation from signal = 2*fIF.
• Image rejection is provided by the RF preselector (tunable BPF before mixer), NOT by the IF filter.
• Higher IF = better image rejection (image farther away) but worse IF selectivity (harder to build sharp IF filter at higher frequencies).
• IRR formula: 20*log10(sqrt(1 + (Q * x)^2)) where x = fimg/fs - fs/fimg.
• AM standard IF = 455 kHz. FM standard IF = 10.7 MHz. These are fixed values to remember for GATE.
• Exam trap: image rejection cannot be improved by increasing IF amplifier gain or Q. Only preselector Q and IF value matter.
• Double conversion receivers use two IFs to simultaneously achieve good image rejection (high first IF) and good selectivity (low second IF).