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# Voltage control oscillator VCO

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VCO used frequently in FM transmitter for modulation.
In Fig.VCO shown below I cut the VCO section from a FM transmitter (http://hem.passagen.se/communication/bug_rf.html) for discussion.
VCO start from BB149A and end at the emitter of T1. BB149A, 3.9 pF, 15 pF and L1 make LC circuit with C varied with the i/p voice signal.
My question is if we assume (for discussion) that no voice at all (i.e. capacitance of BB149 is constant value) then the frequency is constant. How we calculate it, explain with math expression.
Or can you give me a method to design VCO like that shown in the figure.
thanks very much.

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Look up the capacitance of the varactor for the voltage shown on the circuit diagram from the datasheet.

Calculate the value of the capacitance in parallel with L1 by using the formulae I gave you in the other thread.

Calculate the inductance of L1 by using the formulae given here.

Calculate the resonant frequency and there by the frequency of the oscillator using the following formula:
F = 1/(2pi*root(LC))

Where:
C is the value of the capacitance.
L is the inductance.

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Alun

please reread my question carefully before you trying answer. OK i am weak in ENGLISH but i think my question is obvious.
thank you
walid

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What did you want to know?

How to calculate the frequency of the VCO?

The formulae above show this, is there something you don't understand?

You'll need to get the effective capcitance of the diode and the other capacitors in the tuned circuit first, I've explained this here.

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yes Mr Alun i want to calculate LC but the problem is in C itself.
Is Ceq = (15p in series with 3.9p) // (varactor capacitance)
OR Ceq = the three elements in parallel.
THIS IS MY QUESTION.

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Hi there boys

Its not that simple, there is 3 caps to the right of the coil too, they will also affect the resonance frequency! The math in itself is very simple! Lets asume for a while that the capacitance of the varicap is 20 pF. Then the math is as follow:

(1/(1/20pF+1/3.9pF))+15pF+(1/(1/1nF+1/20pF+1/10pF))

That is the total capacitance over the coil. Hope that was right! But then you have to take into account the stray cap also and no math in the world can calculate that properly! When you then calculate the coil you also have to take into account the stray inductance, it can be fairly high at this freqs! A good layout is essential here!

Now Walid, you have to do the math an publish it here, so we can see if it is right!

//Staigen

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Hi Staigen
Thank you very very much for this great explaination
Ceq = (1/(1/20pF+1/3.9pF))+15pF+(1/(1/1nF+1/20pF+1/10pF)) as you said
Ceq =      (3.2636pF)    +15pF+      (0.8696pF)
ceq = 19.133 pF

Now there are three caps to the left of L and three caps to the right of it.
To calculate L i use this equation:

L = 0.001 N2r2 / (228r + 254l)

where L is the inductance in henrys,
r is the coil radius in metres,
l is the coil length in metres (>0.8r) and
N is the number of turns.
In FM Tx the auther give these values about the coil: phi =7.2 mm, n = 3
so r = 7.2/2 = 3.6 mm
0.8 r = 2.88 mm, so length of coil must be > 2.88 lets take it 3 mm ==>

L = 0.001 (9)(1.296 E -5)/[(228 * 0.0036) + (254 * 0.003)]
L = 1.1664 E-7          /[  0.8028      +      0.762  ]
L = 1.1664 E-7          /[          1.5648            ]
L = 0.7454 nH

freq.= 1/[2 * pi * sqr(LC)]
= 1/[2 * pi * sqr(0.7454 nH * 19.133 pF)]
= 1/[2 * pi * sqr(1.42617 E -18)]
= 1/[2 * pi * 1.19422 E -9]
= 133.27 MHz which is out of the intended band (88 - 108 MHz)
Three propabilities:
1) a mistake in my calculations
2) the assumption that the capacitance of the varicap is 20 pF is wrong
3) the coil must be larger value

Still one point: I never think that the three caps to the left of the coil are in relation to the LC calculations.
and still unbeleive thougy the serve to enlage the total C (parallel) and lower the freq.
why not to look at these three caps with L as an independent stage that connected to the folowing (T1) through a coupling cap 1nF.
I think that the auther think that way.

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The reason your value is slightly higher is because there is more capacitance in the tuned circuit than just the physical capacitors in the circuit, there are other parasitic capacitances in the coil and leads that lower the frequency and you can't account for these in your calculations.

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It isn't built yet but its freq. calculates too high.
Yeah, the error in the maths will be cancelled by stray capacitance. ;D

Hi

Ceq =
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Hehe thank you staign but still........

Still one point: I never think that the three caps to the left of the coil are in relation to the LC calculations.
and still unbeleive thougy the serve to enlage the total C (parallel) and lower the freq.
why not to look at these three caps with L as an independent stage that connected to the folowing (T1) through a coupling cap 1nF.
I think that the auther think that way.
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i want mor info about designing a VCO
to Audioguru only
put the analysis and calculations of you FM Tx cicuit

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Hi Walid,
I am sorry but I am not going to analyse and calculate my FM transmitter circuit.
I designed it by using experience, and from copying others.

If you look on the web you will find hundreds of FM transmitter circuits, and they all use the same tuned circuits and many of the entire circuits are also exactly the same.

I designed my circuit in 4 stages:
1) I built the circuit that someone complained about, it didn't work with a new 9V battery, and also didn't work when the battery was a little old.
2) I added a low-dropout voltage regulator so that the supply voltage for the audio preamp and oscillator transistors was stable until the battery was dead. I changed the biasing to operate on the new regulated voltage.
3) Its RF frequency drifted all over the place when anything got near its antenna. So I added an RF buffer/amplifier stage to isolate the oscillator from the antenna.

I built it with a very compact layout to minimise stray capacitance and inductance. I used good-at-high-frequencies 1000pF ceramic supply bypass caps.

I was amazed that it sounded so good. When it transmitted the sound that it picked-up from my home stereo playing an FM radio station, it sounded exactly the same as that station when received on my good car radio. ;D

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Hi

Still one point: I never think that the three caps to the left of the coil are in relation to the LC calculations.
and still unbeleive thougy the serve to enlage the total C (parallel) and lower the freq.
why not to look at these three caps with L as an independent stage that connected to the folowing (T1) through a coupling cap 1nF.
I think that the auther think that way.

This you will have to explain a little bit moore

Also, i have done my math on the 3 caps to the right, they are somewhere around
6,622516556291390728476821192053pF

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To Staigen

(1)
Quote [i usally dont calculate coils and resonanses the way you did here, i use a nomogram for this.]
I also use MATHCAD program, i made many pages to calculate any thing like LC and others, but i do what you see because there are other people read what we are writting so I put them into my account.

(2)
Quote [You almost always have to tweak the coil to get the right freq in a circuit like this, or you can get a adjustable coil(usally reduce Q) or, like Audioguru did, get a trimcap]
I know that stretching the coil decrease L and compressing it increase L.
I don't understand this "usally reduce Q". This you will have to explain a little bit moore
(3)
Quote [A 4) strays! They can easily lower the freq that amount]
I think stray capacitances are not taken into account during calculations, and their effect can be compensated by making the cap variable or L.
(4) Quote[This you will have to explain a little bit moore]
you said this when I try to ask about this: I think that (not sure) only the three caps to the left with L making the LC circuit, then this group connected to the next stage (T1 and related components) through the 1nF.
I know that if we agree about this the freq will be more than 133MHz and this will increase the problem, but i can't accept the three caps to the right to be a part of the LC circuit. please STAIGEN explain this for me. thanks.

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To AUDIOGURU
(1) Quote [1) I built the circuit that someone complained about, it didn't work with a new 9V battery, and also didn't work when the battery was a little old.]
Are you mean that when the battery become less than 9V old

(2) Quote [2) I added a low-dropout voltage regulator so that the supply voltage for the audio preamp and oscillator transistors was stable until the battery was dead]
Are you mean by low-dropout voltage regulator that regulator small size looks like small signal transistor or what?

(4) Quote [i used good-at-high-frequencies 1000pF ceramic supply bypass caps.]
Are these caps polyster caps or what?

(5) Quote [i was amazed that it sounded so good. When it transmitted the sound that it picked-up from my home stereo playing an FM radio station, it sounded exactly the same as that station when received on my good car radio.]
It seems that you put your home stereo near the Tx MIC not connecting it internally to your Tx.

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Hi Walid,
1) The FM transmitter circuit that someone complained about didn't have enough DC negative feedback in its mic preamp to work properly when its battery voltage was above 8V nor if it was below 7V.

2) An ordinary 5V voltage regulator needs an input voltage of 8V or more to operate perfectly. A low-dropout 5V voltage regulator like the one I used needs an input voltage of only 5.5V or more to operate perfectly. I also selected the small plastic case version that looks like a small transistor.

3) Treble is medium and high audio frequencies.
When they designed FM broadcasting, in order to have an extremely low noise level and low distortion, they planned to boost the treble frequencies called pre-emphasis for transmitting and cut the treble frequencies, the noise and some distortion in FM radios. Therefore all FM radios reduce treble frequencies, called de-emphasis. Most simple FM transmitters don't have pre-emphasis so they sound muffled without treble when received on FM radios.

4) Fairly low value ceramic capacitors are very good at very high RF frequencies. Polyester capacitors are good at audio frequencies. A very big difference.

5) Electret mics are pretty good. The electret mic in my pretty good FM transmitter picked-up (in the middle of the room) the sound from my pretty good home stereo. When received on my pretty good car radio, it sounded Pretty Good. ;D ;D

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:)Hehe, Pretty Good Old Man Audioguru! Hehe :) :)

//Staigen

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Hey Sraigen,
Thanks.
I've been there, done that. It's called experience. 8)

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I know, you are good at electronics, and you are some kind of expert, but, as all experts, you also make misstakes sometimes! I do that too, often sometimes, and i mostly have to pay for it! Hehe :) ;) :D ;D

//Staigen

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Sure good guys make mistakes.
The Hubbell space telescope was designed and built by an entire team of experts.
Someone made a big, expensive to fix mistake! :o

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Hehehehe! ;D ;D ;D

//Staigen

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