Superheterodyne Receiver (with MATLAB + Simulator)

Suppose a superheterodyne receiver's intermediate frequency (IF) is tuned to a specific frequency, such as 455 kHz. In this case, the receiver acts as a mixer, generating two different frequencies: F_{LO} + F_{RF} and F_{LO} - F_{RF}, where:

• F_{LO} is the Local Oscillator frequency.
• F_{RF} is the Radio Frequency signal being received.

The Local Oscillator frequency F_{LO} is typically set such that F_{LO} = F_{RF} + F_{IF}, where F_{IF} is the Intermediate Frequency (e.g., 455 kHz in this case).

The intermediate frequency signal carries the same modulation (audio or other data) as the original F_{RF}, but at 455 kHz. This is similar to Double Sideband Suppressed Carrier (DSB-SC) or Single Sideband Suppressed Carrier (SSB-SC) modulation. In SSB-SC, the signal’s upper sideband (from f_c to f_c + f_m) or lower sideband (from f_c - f_m to f_c) contains the modulated information.

Superheterodyne Receiver: Concept and Example

A superheterodyne receiver converts an incoming radio frequency (RF) signal to a fixed intermediate frequency (IF) so that filtering and demodulation become easier.

1. Incoming Signal (RF)

The example uses a 1 MHz AM radio station:

f_RF = 1,000 kHz

2. Local Oscillator Frequency (LO)

The IF is fixed at 455 kHz for AM radios. The local oscillator follows:

f_LO = f_RF + f_IF

Substitute values:

f_LO = 1000 + 455 = 1455 kHz

3. Mixing (Heterodyning)

The mixer produces sum and difference frequencies:

f_sum  = f_LO + f_RF
f_diff = |f_LO - f_RF|

Compute values:

f_sum = 1455 + 1000 = 2455 kHz
f_IF  = 1455 - 1000 = 455 kHz

Only the IF (455 kHz) is kept.

4. AM IF Signal Equation

The intermediate frequency signal carries the same modulation (audio) but at 455 kHz:

v(t) = [1 + m(t)] · cos(2π · 455000 · t)

5. Demodulation

A. Rectification (Envelope Detection)

A diode removes the negative part:

v_rect(t) = |[1 + m(t)] · cos(2π · 455kHz · t)|

B. Low-Pass Filtering

A capacitor & resistor remove the 455 kHz carrier, leaving only the audio envelope:

v_audio(t) ≈ m(t)

6. Final Output

The recovered audio (e.g., a 1 kHz tone) is amplified and sent to the speaker.

Further Reading

1. MATLAB Code for Superheterodyne Receiver
2. Superheterodyne Receiver Online Simulator 
3. Discriminator Receiver