# Operation of LC circuit in Frequency Modulation with simulation and linking it to the basic principle of frequency modulation [duplicate]

Can somebody help how message signal (words spoken near microphone) is modulated using LC circuit and how lc circuit oscillates at particular frequency by applying dc voltage. In the below circuit l1 is 0.1 uH and capacitor is vc10-100 pf.

Actually in frequency modulation increase in voltage of message signal increases the frequency of carrier frequency and decrease in the voltage of message signal decreases the carrier frequency .I want that concept to be linked to the circuit. Thanks in Advance

• Mar 18, 2016 at 18:32
• But i do not find required answer there Mar 18, 2016 at 18:34
• Then you really need to be very specific with the question you are asking. Mar 18, 2016 at 18:39

Andy is correct but perhaps it would be easier to look at a picture of what happens.

What you don't see in the circuit diagram is the collector-base 'capacitor' which varies according to the audio input signal. This effect is multiplied by the transistor (in the old days this effect was first seen in valves). The change in capacitance follows the audio signal.

In the second diagram we re-arrange the circuit to look at the equivalent AC circuit. C1 shorts out the base and MIC1 to ground and of course the positive and negative rails (to AC) are the same connection. This leaves the miller capacitance in parallel with the tank circuit. Changes in the miller capacitance (following the audio signal) change the resonant frequency of the tank circuit.

This isn't a particularly good circuit (linear, well behaved etc.) but it works for a simple FM bug.

• Will the tank circuit be oscillating at a particular frequency without the application of sound signal? Thanks in advance Mar 18, 2016 at 19:20
• Yes, there is a capacitance contribution from the transistor even without an audio input . However, this contribution is still parallel to VC1 and simply gives a minimum capacitance value, along with any stray capacitances in the circuit, even if VC1 is set to zero . For tuning purposes the actual values for L1 and tuning capacitance will only be approximate so don't get too hung up trying to separate the different components. Treat the tank circuit values as lumped values and apply the resonant frequency formula for a parallel LC circuit. Mar 20, 2016 at 14:35

Inside the BJT is the miller capacitor and this capacitor (for AC signals) can be shown to be effectively in parallel with the tank circuit. The miller capacitor can be altered by the application of different base-collector voltages hence a signal on the base can dynamically change the miller capacitor and cause the carrier frequency to become modulated with the audio signal. It's not a great FM circuit but it does work with some distortion on the demodulated signal.

• Could you draw a rough diagram of miller capacitor and tank circuit .So that it becomes more clear .Thanks in advance Mar 18, 2016 at 19:03

• A condenser microphone is used to accept the sound signals. Inside the mic, a capacitive sensor diaphragm is present. It vibrates according to the air pressure changes and generates AC signals.

• The inductor L1 and variable capacitor (trimmer) forms an oscillating tank circuit along with the transistor BC547. It is the common NPN transistor used for general purpose amplifications.

• As long as the current exists across the inductor coil L1 and the variable capacitor, the tank circuit will oscillate at the resonant carrier frequency for FM modulation. Capacitor C2 acts as a negative feedback to the oscillating tank circuit.

• Every FM transmitter circuit requires an oscillator part to generate the radio Frequency (RF) carrier waves. The name ‘Tank’ circuit is derived from the capacity of the LC circuit to store energy for oscillations.

• The input audio signal from the mic is fed to the base of transistor which modulates the LC tank circuit carrier frequency in FM format.

• The variable capacitor is used to change the resonant frequency for fine adjustment to the FM frequency band.

• The modulated signal from the antenna is radiated as radio waves at FM frequency band. Antenna is nothing but a simple copper wire of 20 cm long and 24 gauge.

• The length of the antenna is very significant in the FM transmitter circuit. Here you can use a 25-27 inches long copper wire as antenna.

Anything else?

• Thanks but how ac signal is oscillated by using lc circuit .Can you link oscillation to frequency modulation principle Mar 18, 2016 at 18:31
• Cbc parasitic capacitance is the main cause for FM modulation in this circuit. And Cbc changes his value due to amplitude change thanks to the signal from the microphone. And Cbc for the AC signal is in parallel with VC1 capacitor and this is why we have FM modulation together with unwanted AM modulation.
– G36
Mar 18, 2016 at 18:32