Here the working of an FM transmitter circuit that uses a two-stage amplifier and an LC tank circuit to generate and modulate a carrier wave is explained in details. The audio signal from the microphone modulates the frequency of the carrier wave, producing an FM signal that is transmitted via the antenna. The equations provided explain the resonant frequency and frequency modulation process.
Circuit Description
1. Electret Microphone and Pre-Amplifier Stage
Electret Microphone:
The microphone is pulled up with a 4.7 kΩ resistor (R1) to provide bias voltage.
The audio signal from the microphone is coupled to the pre-amplifier stage via a 22 nF capacitor (C1).
Pre-Amplifier (Q1):
The pre-amplifier is built using a BC547 transistor (Q1).
Self-Biasing:
A 1 MΩ resistor (R2) is connected from the collector to the base for biasing.
The collector is connected to the 6V supply through a 22 Ω resistor (R3).
The emitter is grounded.
The pre-amplifier amplifies the weak audio signal from the microphone.
2. Second Amplifier Stage (Q2)
The amplified signal from the collector of Q1 is coupled to the base of another BC547 transistor (Q2) via a 100 nF capacitor (C2).
Biasing:
The base of Q2 is pulled high with a 100 kΩ resistor (R4).
The base is also grounded with a 1 nF capacitor (C4) to stabilize the bias voltage.
Emitter Resistor:
The emitter of Q2 is grounded through a 470 Ω resistor (R5).
A 27 pF bypass capacitor (C5) is connected across R5 to stabilize the emitter voltage for high-frequency signals.
3. LC Tank Circuit
The LC tank circuit consists of:
Capacitor (C): 30 pF trimmer
Inductor (L): 218.29 nH.
The LC tank is connected to the collector of Q2 and determines the carrier frequency of the FM transmitter.
4. Feedback and Oscillation
A capacitor (C6) is connected between the collector and emitter of Q2 to provide positive feedback for sustaining oscillations.
5. Antenna
The antenna (170 cm) is directly connected to the collector of Q2 to radiate the FM signal.
How the Circuit Works
Pre-Amplifier Stage (Q1):
The electret microphone converts sound into an electrical signal.
The 4.7 kΩ resistor (R1) provides bias voltage to the microphone.
The 22 nF capacitor (C1) couples the audio signal to the base of Q1.
Q1 amplifies the audio signal, which is then coupled to the base of Q2 via the 100 nF capacitor (C2). See how to build Electret Microphone Preamplifier.
Second Amplifier Stage (Q2):
Q2 further amplifies the signal and acts as the oscillator.
The LC tank circuit (30 pF and 218.29 nH) generates the carrier wave at the desired FM frequency.
Frequency Modulation:
The audio signal from the microphone modulates the base voltage of Q2.
This modulation causes the base-collector capacitance () of Q2 to vary, changing the resonant frequency of the LC tank circuit.
The result is a frequency-modulated (FM) signal.
Transmission:
The antenna radiates the FM signal into the air. See the guide how to make FM Transmitter. The output power is around 10mW.
Equations for Frequency Modulation
1. Resonant Frequency of the LC Tank Circuit
The resonant frequency () of the LC tank circuit is given by:
Where:
= inductance (54 nH).
= capacitance (30 pF).
Substitute the values:
2. Frequency Modulation
The instantaneous frequency of the FM signal is given by:
Where:
= carrier frequency (100 MHz).
= frequency deviation (depends on the amplitude of the audio signal).
= frequency of the audio signal (e.g., 550 Hz).
3. Frequency Deviation ()
The frequency deviation depends on the modulation index () and the audio signal frequency:
Where:
= modulation index (typically 1–5 for FM broadcasting).
Key Points
Carrier Frequency:
The LC tank circuit generates a carrier wave at 100 MHz.
Frequency Modulation:
The audio signal modulates the base voltage of Q2, causing the carrier frequency to vary.
Transmission:
The antenna radiates the FM signal, which can be received by an FM radio.
