Resonant Frequency

Have you considered building the circuit and measuring the frequency?

i want to calculate its resonant frequency not measure it.

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.

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?

Without knowing what is loading the output connection, the problem is 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.

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.

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)

Please post the complete circuit.

here is the complete circuit; it is a vco

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?

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

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

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

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 a radio-frequency choke. 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?

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

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

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.

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

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

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.