How Direct FM works with Single Transistor

 In direct FM the carrier signal frequency is varied in accordance to the message amplitude. Consider the following single BJT transistor FM transmitter circuit shown below. The BJT 2N3904 is an oscillator and frequency modulator. The transistor together with inductor L1, capacitors C2,C3,C6 and resistors R2,R3 forms the frequency modulator.

The C3 10 pF capacitor between the collector and emitter in the FM transmitter circuit serves two primary purposes: positive feedback to sustain oscillations and stabilization of the oscillator. Let’s break down how it works and whether it affects the total capacitance of the LC tank circuit.

1. Role of the 10 pF Capacitor

Positive Feedback:

• The 10 pF capacitor provides a path for a small portion of the signal from the collector to be fed back to the emitter.

• This feedback is positive because it reinforces the oscillations in the LC tank circuit, ensuring that the circuit continues to oscillate.

• Without this feedback, the oscillations would die out due to losses in the circuit.

Stabilization:

• The capacitor helps stabilize the oscillator by reducing high-frequency noise and preventing unwanted oscillations or spurious signals.

2. Effect on the Total Capacitance of the LC Tank

The 10 pF capacitor is not directly part of the LC tank circuit. The LC tank consists of the 80 nH inductor and the 30 pF trimmer capacitor. However, the 10 pF capacitor can have an indirect effect on the LC tank circuit due to its connection between the collector and emitter.

Indirect Effect:

• The 10 pF capacitor forms a feedback network with the transistor, which can slightly alter the effective capacitance seen by the LC tank circuit.

• This effect is typically small and is often neglected in simple calculations. However, in high-frequency circuits, even small capacitances can influence the behavior of the circuit.

3. How the 10 pF Capacitor Provides Positive Feedback

Transistor Operation:

• The transistor in your circuit operates as a common-emitter amplifier. In this configuration, the signal at the collector is 180° out of phase with the signal at the base.

• The 10 pF capacitor feeds a portion of the collector signal back to the emitter.

Phase Shift and Feedback:

• The emitter is effectively at AC ground due to the 27 pF capacitor connected between the emitter and ground.

• The feedback signal from the collector to the emitter introduces a phase shift that, when combined with the inherent phase shift of the transistor, results in positive feedback.

• This positive feedback ensures that the energy lost in the LC tank circuit is replenished, sustaining oscillations as required by electronic oscillator.
  

4. Mathematical Explanation of Positive Feedback

Gain and Feedback:

• For oscillations to occur, the loop gain of the circuit must satisfy the Barkhausen criterion:

  $$\mathrm{\mid }A\beta \mathrm{\mid }\ge 1$$

  Where:

  • $A$ = gain of the amplifier (transistor).

  • $\beta$ = feedback factor (determined by the 10 pF capacitor).

• The 10 pF capacitor ensures that the feedback factor ($\beta$) is sufficient to meet this criterion.

Phase Condition:

• The total phase shift around the loop must be 0° or 360° for positive feedback.

• The transistor provides a 180° phase shift, and the LC tank circuit provides an additional 180° phase shift at resonance, satisfying the phase condition.

5. Practical Considerations

Effect on Frequency:

• The 10 pF capacitor can slightly affect the resonant frequency of the LC tank circuit due to its connection to the transistor.

• However, this effect is usually small and can be compensated by tuning the 30 pF trimmer capacitor.

Stability:

• The 10 pF capacitor helps stabilize the oscillator by reducing high-frequency noise and preventing unwanted oscillations.

• It also ensures that the oscillator starts reliably and maintains stable oscillations.

6. Example of Feedback in Action

Imagine the LC tank circuit is oscillating at its resonant frequency ($f_c$). The following happens:

1. The LC tank generates a signal at the collector.

2. A small portion of this signal is fed back to the emitter through the 10 pF capacitor.

3. The feedback signal reinforces the oscillations, ensuring that the energy lost in the LC tank is replenished.

4. The transistor amplifies the signal, and the process repeats, sustaining oscillations.