Bandwidth of simple FM transmitter given in schematic?

Question

The following circuit is a basic FM transmitter, which broadcasts for a limited range of about 10 meters. It is tuned by an LC tank circuit, where the capacitor is a trimmer one. I want to know the Q factor for this transmitter and how it can be calculated and if possible with the values that are given in this example. All I know is that calculation of Q factor should need an inductor and capacitor, which are already given, but the resistor does not exist in this tank circuit. Where can I get this needed one from this circuit for calculation Q factor? What is the bandwidth of this FM transmitter and how to calculate it? The following picture describes this circuit:

the Ltspice file .asc:

Version 4
SHEET 1 928 680
WIRE 544 -128 256 -128
WIRE 544 -96 544 -128
WIRE 256 -64 256 -128
WIRE 256 -64 32 -64
WIRE 256 -16 256 -64
WIRE 256 -16 112 -16
WIRE 368 -16 256 -16
WIRE 432 -16 368 -16
WIRE 32 0 32 -64
WIRE 368 0 368 -16
WIRE 432 0 432 -16
WIRE 368 16 368 0
WIRE 544 32 544 -16
WIRE 368 96 368 64
WIRE 432 96 432 80
WIRE 432 96 368 96
WIRE 32 112 32 64
WIRE 368 112 368 96
WIRE 464 112 368 112
WIRE 560 112 464 112
WIRE 368 128 368 112
WIRE 464 144 464 112
WIRE 112 176 112 64
WIRE 112 176 0 176
WIRE 192 176 112 176
WIRE 304 176 192 176
WIRE 368 240 368 224
WIRE 464 240 464 208
WIRE 464 240 368 240
WIRE 112 256 112 176
WIRE 368 256 368 240
WIRE 192 272 192 176
WIRE 112 400 112 336
WIRE 112 400 0 400
WIRE 192 400 192 336
WIRE 192 400 112 400
WIRE 368 400 368 336
WIRE 368 400 192 400
WIRE 192 496 192 400
FLAG 192 496 0
FLAG 544 32 0
FLAG 560 112 out
FLAG 32 112 0
FLAG 0 176 audio_POS
FLAG 0 400 audio_NEG
SYMBOL res 96 -32 R0
SYMATTR InstName R1
SYMATTR Value 4.7k
SYMBOL res 96 240 R0
SYMATTR InstName R2
SYMATTR Value 1k
SYMBOL res 352 240 R0
SYMATTR InstName R3
SYMATTR Value 330
SYMBOL npn 304 128 R0
SYMATTR InstName Q1
SYMATTR Value BF199
SYMBOL cap 16 0 R0
SYMATTR InstName C1
SYMATTR Value 22n
SYMBOL cap 352 0 R0
SYMATTR InstName C2
SYMATTR Value 22p
SYMBOL ind 416 -16 R0
SYMATTR InstName L1
SYMATTR Value 0.2µ
SYMBOL cap 448 144 R0
SYMATTR InstName C3
SYMATTR Value 22p
SYMBOL cap 176 272 R0
SYMATTR InstName C4
SYMATTR Value 1n
SYMBOL voltage 544 -112 R0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName V1
SYMATTR Value 9V
TEXT -50 520 Left 2 !.tran 0 100u 99u 500n
TEXT 120 424 Left 2 ;R2 can vary till 4.7k as tested already..
TEXT 624 32 Left 2 ;L1 -> \n0.75cm former diameter\n1mm wire\n5mm length
TEXT -232 288 Left 2 ;audio can be an mp3 player
TEXT 424 256 Left 2 ;C3 may be 4.7pF as well, but output varies.
TEXT 280 -64 Left 2 ;Output frequency:\n70MHz - 105MHz

Answer 1

Where can I get this needed one from this circuit for calculation Q factor?
What is the bandwidth of this FM transmitter and how to calculate it?

I should try to answer (simplest) your question by simulation.
This has a mathematical background, but perhaps a "bit" complicated.
Made with microcap v12.

AC Analysis, bandwidth = ~ 2.2 MHz

Transient Analysis (after the start delay for working ...)
Note that you have already a modulation with 0.1 Vpp BF input.
The 0.25 Vpp input should be "over" modulation ...
This shows only the AM modulation.
This can not show the FM modulation ... A demodulator would be needed.

Answer 2

I want to know the Q factor for this transmitter and how it can be calculated and if possible with the values that are given in this example.

• The transistor collector has an output impedance that is usually in the kΩ range. it is effectively in parallel with the tank circuit.
• The feed into the emitter is a low resistance and is a parallel loss in series with 22 pF (C3)
• The electrical resistance of the inductor is a series loss
• The output wire / antenna is also a loss-bringing element in that real power has to be taken from the transmitter if you are to receive something. It might have an equivalent resistance anywhere from 1 Ω to over 1 kΩ (length dependent)

All the above reduce the q-factor of the circuit.

Where can I get this needed one from this circuit for calculation Q factor?

It's not just one resistor; it's a bunch of parallel and series resistors all acting together to lower and define the true q-factor.

What is the bandwidth of this FM transmitter and how to calculate it?

I would model it in a simulator and do some work trying to figure out what the effective parallel loss and reactance of the antenna is (likely to be dominant). The length of the antenna is key here.