Secondary Image Calculator

Overview

The problem of the second image frequency arises in superheterodyne receivers with two downconversion steps since the second downconverter also has an image frequency which needs to be filtered at the RF frontend.

This calculator determines the local oscillator (LO) frequencies and image frequencies for both stages of a dual-conversion superheterodyne receiver using low-side injection.

In a downconversion mixer, two frequencies lie in the same intermediate frequency:

  • The intended intermediate frequency: \(f_{IF} = f_{RF} - f_{LO}\)

  • The image frequency (from the negative side of the spectrum): \(-f_{IM} + f_{LO} = f_{IF}\)

Dual-Conversion Receiver Architecture

A dual-conversion receiver performs frequency conversion in two stages:

  1. First Stage: RF signal → 1st IF

  2. Second Stage: 1st IF → 2nd IF

General Formula (Low-Side Injection)

In mixers with low-side injection, the following equation applies:

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

First Conversion Stage (RF → 1st IF)

LO1 Frequency:

\[f_{LO1} = f_{RF} - f_{IF1}\]

The image frequency comes from the negative side of the spectrum and falls in the IF band:

\[f_{IF1} = -f_{IM1} + f_{LO1}\]

Therefore:

First Image Frequency:

\[f_{IM1} = f_{LO1} - f_{IF1}\]

Second Conversion Stage (1st IF → 2nd IF)

LO2 Frequency:

\[f_{LO2} = f_{IF1} - f_{IF2}\]

Similarly, the second image frequency is:

Second Image Frequency:

\[f_{IM2} = f_{LO2} - f_{IF2}\]

Example Calculation

Parameter

Value

RF Frequency

800 MHz

1st IF Frequency

200 MHz

2nd IF Frequency

10 MHz

First Stage Results:

  • \(f_{LO1}\) = 800 - 200 = 600 MHz

  • \(f_{IM1}\) = 600 - 200 = 400 MHz

Second Stage Results:

  • \(f_{LO2}\) = 200 - 10 = 190 MHz

  • \(f_{IM2}\) = 190 - 10 = 180 MHz

Why Not Just One IF?

Choosing an IF frequency is a trade-off between image rejection and selectivity:

High IF

Pros

Cons

Large separation between desired signal and image: The image can be rejected with a simple filter

Narrow, high-Q filters are still needed at the IF, and they are difficult to build at high frequencies

Low IF

Pros

Cons

Easier to build high rejection filters

Image frequency is close to the wanted signal, so image rejection at RF becomes difficult

Note

Solution: Dual conversion uses a high first IF and then a low second IF

Role of the Second IF

Once the signal is at the first IF:

  • The first IF filter is relatively wide and mainly cleans up mixer products and distant interferers

  • The second mixer converts this first-IF signal down to a much lower second IF

At the second IF, high selectivity filters are needed, but they are cheaper to build than at higher frequencies.