Image Frequency Calculator | Qucs-S S-parameter Viewer Documentation

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# Image Frequency Calculator

In a superheterodyne receiver, the image frequency is an unwanted frequency that, when mixed with the local oscillator (LO), produces the same intermediate frequency (IF) as the desired RF signal.

Note

Problem: Consequently, if it is not properly filtered out before the mixer, any signal present in the image band will appear at the IF output along with the wanted signal, causing interference.

## How Mixers Work

A mixer produces sum and difference frequencies:

\[f_{out} = |f_{RF} \pm f_{LO}|\]

For downconversion purposes:

\[f_{IF} = |f_{RF} - f_{LO}|\]

## Injection Modes

### Low-Side Injection

The LO frequency is below the RF frequency:

\[f_{IF} = f_{RF} - f_{LO}\]

Then:

\[f_{LO} = f_{RF} - f_{IF}\]

The image frequency is taken from the negative side of the spectrum:

\[f_{IF} = -f_{IM} + f_{LO}\]
\[\mathbf{f_{IM} = f_{LO} - f_{IF} = f_{RF} - 2 \times f_{IF}}\]

### High-Side Injection

The LO frequency is above the RF frequency:

\[f_{IF} = f_{LO} - f_{RF}\]

Then:

\[f_{LO} = f_{RF} + f_{IF}\]

The image frequency in high-side injection comes from the positive side of the spectrum and fall in the IF frequency but in the negative side of the spectrum:

\[-f_{IF} = f_{IM} - f_{LO}\]
\[\mathbf{f_{IM} = f_{RF} + 2 \times f_{IF}}\]

Why? Because $f_{LO} - f_{IM} = f_{IF}$

## Example Calculation

Parameter | Value
--- | ---
RF Frequency | 1000 MHz
IF Frequency | 200 MHz

### Low-Side Injection

- $f_{LO} = 1000 - 200 = \mathbf{800\ MHz}$

- $f_{IM} = 1000 - 2 \times 200 = \mathbf{600\ MHz}$

Verification: 800 - 600 = 200 MHz ✓

### High-Side Injection

- $f_{LO} = 1000 + 200 = \mathbf{1200\ MHz}$

- $f_{IM} = 1000 + 2 \times 200 = \mathbf{1400\ MHz}$

Verification: 1400 - 1200 = 200 MHz ✓

## Choosing the IF Frequency: The Trade-Off

### High IF

Pros | Cons
--- | ---
• Large separation ($2 \times f_{IF}$) between signal and image • RF preselector can easily reject the image • Simpler, cheaper RF filters required | • Harder to build very narrow, high-Q channel filters at high frequency • Poor adjacent-channel selectivity • More expensive components

### Low IF

Pros | Cons
--- | ---
• Easy to build very narrow, high-quality filters • Excellent adjacent-channel selectivity • Better performance and lower cost | • Small separation between signal and image • Image frequency is close to wanted signal • May require sharp, expensive RF preselection