Superheterodyne Receiver

The superheterodyne receiver is the dominant radio receiver architecture used in virtually all modern AM, FM, and communication receivers. It solved the fundamental selectivity and gain problems of the TRF receiver by converting any incoming signal to a fixed intermediate frequency before amplification and demodulation.

Core Concept: Frequency Conversion

The superheterodyne receiver works on the principle of frequency conversion. Instead of amplifying the incoming RF signal at whatever frequency the station broadcasts, the receiver multiplies the RF signal with a locally generated sinusoid from a local oscillator (LO). This multiplication produces sum and difference frequency components. A bandpass filter then selects only the difference frequency component, which is called the intermediate frequency.

Because the LO frequency is always adjusted to be exactly fIF above the desired station frequency, the difference frequency is always the same fixed value regardless of which station is tuned. This means all the IF amplifier stages and the IF bandpass filter operate at a constant center frequency. Selectivity and gain are therefore constant across the entire tuning band, solving the TRF bandwidth variation problem completely.

The word superheterodyne comes from combining supersonic (frequencies above audio) and heterodyne (mixing two frequencies to produce a new one). The mixing process is fundamentally a multiplication in the time domain, which corresponds to convolution of spectra in the frequency domain.

Mixer and IF Amplifier

The mixer is a nonlinear or time-varying element that multiplies the incoming RF signal with the LO signal. If the RF signal is A*cos(2*pi*fs*t) and the LO is B*cos(2*pi*fLO*t), the mixer output contains components at (fLO + fs) and (fLO - fs). The IF bandpass filter selects the component at fIF = fLO - fs, rejecting the sum component.

The IF amplifier provides the bulk of the receiver's gain. Since it operates at a fixed frequency, the amplifier can be designed with a carefully tuned, high-Q bandpass response optimized for that one frequency. This gives the superheterodyne its outstanding selectivity. In AM broadcast receivers the standard IF is 455 kHz. In FM broadcast receivers the standard IF is 10.7 MHz.

Mathematical Expression

The frequency relationships in a superheterodyne receiver are governed by three equations. For high-side injection (most common): fLO = fs + fIF, which gives the difference fIF = fLO - fs. The image frequency is the frequency that also produces the same IF when mixed with the LO: fimage = fLO + fIF = fs + 2*fIF. The image must be rejected by the RF filter (preselector) before the mixer. Image rejection ratio depends on how well the RF preselector attenuates the image relative to the desired signal.

Practical Implications

The choice of IF frequency involves a fundamental trade-off. A higher IF places the image frequency farther from the desired signal, making it easier for the RF preselector to reject the image. However, a higher IF requires a wider fractional bandwidth in the IF filter, making it harder to achieve sharp selectivity. A lower IF gives better selectivity in the IF stages but brings the image frequency closer to the desired signal, requiring a sharper RF preselector.

The RF amplifier stage before the mixer serves as a preselector, providing initial selectivity to suppress the image frequency. Without this stage, strong signals at the image frequency would pass through the mixer and appear in the IF passband, causing interference that is indistinguishable from the desired signal.

Given:
AM broadcast receiver
Desired station frequency fs = 600 kHz
Standard IF fIF = 455 kHz

Why this formula applies:
High-side injection: LO is tuned above the signal frequency
fLO = fs + fIF
Image = fLO + fIF = fs + 2*fIF

Formula:
fLO = fs + fIF
fimage = fs + 2*fIF

Substitution:
fLO = 600 kHz + 455 kHz = 1055 kHz
fimage = 600 kHz + 2 * 455 kHz = 600 + 910

Calculation:
fLO = 1055 kHz
fimage = 1510 kHz

Final Answer: LO must be set to 1055 kHz. Image frequency is 1510 kHz, which is 910 kHz away from the desired 600 kHz station and must be rejected by the RF preselector filter before the mixer.

Exam Tip: For high-side injection, fLO = fs + fIF and fimage = fs + 2*fIF. For low-side injection, fLO = fs - fIF and fimage = fs - 2*fIF. In GATE, always check whether high-side or low-side injection is specified before computing image frequency. Standard AM IF = 455 kHz, standard FM IF = 10.7 MHz.

Quick Revision

• Superheterodyne converts incoming RF to a fixed IF using a mixer and local oscillator before amplification and demodulation.
• High-side injection: fLO = fs + fIF. Difference component at fIF = fLO - fs is selected by IF bandpass filter.
• Image frequency: fimage = fs + 2*fIF (high-side). Must be rejected by RF preselector before mixer.
• Standard IF values: 455 kHz for AM broadcast, 10.7 MHz for FM broadcast receivers.
• Advantage over TRF: fixed IF means constant bandwidth, constant gain, and optimized selectivity regardless of tuned station.
• IF amplifier provides most of the gain because it operates at fixed frequency where high-Q tuning is practical.
• Trade-off: higher IF improves image rejection but degrades IF selectivity. Lower IF does the opposite.