# Resonant Frequency

Discussion in 'Electronic Basics' started by redhat, Jun 18, 2005.

2. ### redbellyGuest

Have you considered building the circuit and measuring the frequency?

3. ### Andrew HolmeGuest

You have a series LC circuit with inductor L, capacitor C5, and the
capacitance of varactor D1.

First, you need to know the capacitance of D1. This varies with the DC bias
voltage. In your case, the bias voltage is Vcc. There should be a graph of
capacitance vs voltage on the varactor data sheet.

You can then combine the varactor capacitance with that of C5 using the
equation for capacitors in series:
C = (C1*C2) / (C1+C2)

The resonant frequency of the LC circuit can then be found from :

2*pi*f = 1 / sqrt(LC)

4. ### redhatGuest

i want to calculate its resonant frequency not measure it.

5. ### redhatGuest

Hi redbelly,
i want to calculate its frequency not measure it
Hi Andrew Holme,
this is a resonator fo a vco, the input to the resonator is at the node
connecting D1, L1, and R3 , so, the bias voltage to the varactor is
Vinput+ ( Vcc - I*R3) is that correct? if so, how to calculate the
resonant frequency noting that i don't know I where I is the current in
R3 branch.

6. ### John PopelishGuest

indeterminate. I(f the output is open circuit, the circuit has no
resonance worth mentioning. if the output is a short to ground, the
resonant frequency is the series equivalent capacitance of the
varactor and the variable capacitor with the inductor w=1/(sqrt(L*C)).
If the output has other impedance, there is a different solution.

7. ### redhatGuest

the load to the output is an npn transistor, so i have to take the Cbe
into consideration, what about the Vcc what is its purpose?.. i mean
the varactor bias is from the input voltage so is it to increase its
bias voltage?

9. ### John PopelishGuest

The Vcc bias alters the capacitance of the varactor. It also makes
sure that the varactor stays reverse biased during the signal cycle,
so that the device always looks like a capacitor. If the varactor
ever becomes forward biased, it acts like a low value resistor in
parallel with any junction capacitance.

10. ### redhatGuest

here is the complete circuit; it is a vco
http://www.geocities.com/aezzat3/vco1.jpg
i don't know the capacitance of the varactor because it depends on (
the input voltage + Vcc-IR3) ,so how to know the resonant frequency
equation?

11. ### Don BoweyGuest

The vericap is spec'd with a plot of capacitance:voltage. If you can find
the part number you can obtain that information. Since it is the FM
"modulator," off-hand I think it's capacitance value will not affect the at
rest frequency more than a couple hundred kHz.

Don

12. ### Andrew HolmeGuest

You could have included a bit more to the left!

I'm forced to assume the modulating input is coupled via a large resistor or
I'm also assuming it's AC-coupled.
Correct?

Then the average DC voltage across D1 will be Vcc - get the capacitance from
the datasheet for this voltage. It's probably in the region of a few pF.

The series resonant frequency of D1, L1, C5 can then be found.

I*R3 is negligible.

BTW Is that supposed to be an inductor in Q1 collector?

13. ### redbellyGuest

If you don't know the varactor capacitance, there is no way to
calculate a resonance frequency. The capacitance (as a function
of input voltage) would be found on a spec sheet, if it can be
found anywhere. Do you have a spec sheet for it? If not, have
you looked on the manufacturer's web site? Or searched with Google?

It might be helpful to know if an simplifiying approximation is
valid. Is the input signal small enough so that the capacitance
is largely determined by Vcc? Then you can use THAT capacitance
(as determined by the varactor specs) to determine the resonance
frequency.

If, on the other hand, the input alters the capacitance significantly,
then the behavior is highly nonlinear and probably a numerical
simulation is required to find the resonance. But doing that would
be well beyond the scope of what's describable in a newsgroup, and
possibly more time-consuming than measuring the resonance for a few
different values of L1 and C5.

Mark

14. ### JamieGuest

Fr = 1/2*PI*sqrt(L*C);

15. ### Rich GriseGuest

It's a VCO. "I/P" (presumably in-put), is the DC control voltage,
then, redrawing, it's a simple Hartley oscillator with its output
shorted to VCC - wait a minute..... Maybe they're taking the output
off of ...

There's something wrong with that circuit.

But the resonant frequency is the series resonant frequency:
f = 1 / (2 * pi * sqrt(L * Ct)), where Ct is the value of the
series combination of C5 and the capacitance of D1. The capacitance
of D1 depends on the sum of the input voltage and whatever proportion
of VCC, depending on the impedance presented by the input.

Hope This Helps!
Rich

16. ### redhatGuest

what is wrong with it? isn't this a resonator followed by negative
resistance reflection amplifier? what i don't know is how to calculate
the resonant frequency

17. ### redhatGuest

what is wrong with it? isn't this a resonator followed by negative
resistance reflection amplifier? what i don't know is how to calculate
the resonant frequency because i don't know the portion of voltage
remaining from Vcc.

18. ### Andrew HolmeGuest

The average voltage across the varactor is Vcc. This is the voltage
you should use to lookup its capacitance.

19. ### redhatGuest

how could it be Vcc? this means that the varactor has constant
capacitance, so there is no change in frequency. am i right?

20. ### Andrew HolmeGuest

No. The *average* is Vcc. I'm assuming there will be a small AC
modulating signal superimposed on top, but you can calculate the
carrier frequency of the resultant FM from the average.  