# Transfer function clarification

#### garimella

##### Full Member level 4
A VCO has a transfer function of 100/s, could this mean, it produces frequency which is 100KHz/V?

#### wwfeldman

which VCO?
what does the data sheet say?
what do the applicable ap notes say?
there (likely) is at least one ap note with a sample usage. what does that say?

#### albbg

The Laplace model of a vco is given by the expression

Phase/Vin = Gain/s

where "s" is the Laplace operator

then in you case Gain=100. Trasforming into time domain we have dPhase/dt = Gain*Vin that is w = Gain*Vin

2*pi*frequency = 100*Vin from which frequency/Vin = 100/(2*pi) = 16 Hz/V

#### garimella

##### Full Member level 4
Hi albbg

Suppose the VCO produces output say 1KHz/V (square wave)and I connect it to a 10 bit counter. Then it would take 1 second for counter to roll off. So the time constant is 1 second in this case. Would the transfer function of the combo not be 1/s in this case?

#### KlausST

##### Super Moderator
Staff member
Hi.

What you say can be mathematically shown as:

f = 1 / t
or
t = 1 / f

Klaus

#### garimella

##### Full Member level 4
Hi KlausST

Are you confirming that the expression 1/s is correct?

#### FvM

##### Super Moderator
Staff member
Would the transfer function of the combo not be 1/s in this case?

Unless you arbitrarily redefine the commonly understood VCO transfer function definition, you should consider what albbg told. The unit is rad/s rather than Hz.

#### garimella

##### Full Member level 4
At this point of view, I was wondering the difference between VFC vs VCO?

#### FvM

##### Super Moderator
Staff member
Literally, a VCO is a VFC (voltage to frequency converter) and vice versa. Specifically the term VFC refers to converters with large frequency ratio (e.g. 0 to xx kHz) and high linearity. The frequency ratio of a VCO can range between several 100 ppm (tuned crystal oscillator) to decades (current steered rings oscillator).

#### LvW

A VCO has a transfer function of 100/s, could this mean, it produces frequency which is 100KHz/V?
When the given expression is really the TRANFER FUNCTION (and not thefrequency with s=seconds), it must be interpreted as the PHASE characteristics.
This is because in a linear PLL model the input and output quantities are given as PHASE values.

In this case, the transfer function is PHI(s)=Ko/s
with Ko=VCO constant given in rad/Vs.

#### garimella

##### Full Member level 4
Referring to the thread https://www.edaboard.com/threads/interpretation-of-frequency-of-vco.388688/. Please clarify, if I have VFC such as LM231 which provides linear frequency output , say 100KHz for 0-10V. Then what would be its transfer function with 10 bit counter combo. Now consider VCO which is highly non linear for 0-10V, what should I consider the transfer function as?

#### KlausST

##### Super Moderator
Staff member
Hi,

the transfer function of the LM231 is given in the datsheet. No need to guess...
It is not "100kHz fo 0..10V". You may say it is
* 100kHz/10V (as ratio) or 10kHz/V
* 0...100kHz for 0..10V (as range)
(just as examples)

For non linear transfer functions you need to get the formula or at least a diagram.
There will be flat and steep areas. Now it depends on what you are interested in:
In the dynamics, in the deviation form linear, in the most flat area in the most steep area...
... ignoring or including the offset...

Klaus

#### garimella

##### Full Member level 4
Hi KluasST

So VCO transfer function purely depends on region of operation of frequency. For a VFC , the TF is straightforward as you pointed. I was interested to see how TF changes with 10 bit counter or 12 bit counter in series. My aim is identify TF of this combo

#### KlausST

##### Super Moderator
Staff member
Hi,

I don't understand what a counter has to do with VCO TF..

Klaus

#### FvM

##### Super Moderator
Staff member

VCO gain (e.g. 10 kHz/V) has nothing to do with the delay created by frequency counter period. By adding the counter, you are creating a time and amplitude discrete system which can't be described by the parameters of a time and amplitude continuous VCO.

The frequency counter period is the sampling interval, the VCO gain multiply sampling interval determines the amplitude resolution. Oviously the voltage range will be limited according to VCO gain, maximum count and sampling period.

#### garimella

##### Full Member level 4
I had the following issue is mind before posting this question
1. I had to do system identification of a VFC module whose TF was not known. So one way of doing this is step response and I had to create a model for this. Using a VFC cascaded with counter and DAC. Put the output of DAC in feedback loop to see the response. Indeed the response reaches the steady state for input of 1V, but I was not sure how to estimate the gain of this TF. VFC has its own TF and a counter cascaded should introduce a delay.I presume that VFC ,counter combo will result in TF =k/s, which is quite different from VFC gain as such. So I raised this issue .
So I wanted to know the TF of the combo in this scenario (value of k?) (btw i am using VFC and a counter in an application and TF must be known to model the entire system)

#### FvM

##### Super Moderator
Staff member
k/s is an integrator, that's not the transfer function of the VCO with frequency counter. The sampled counter acts as a time discrete averager not an integrator. The equivalent time continuous transfer function in time domain is sin(x)/x.

#### garimella

##### Full Member level 4
Hi FVM

Had a quick check in matlab and through simulation, it appears that the transfer function of VCO counter combo is k/s, where k is reciprocal of time constant, T=clk * counts

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#### FvM

##### Super Moderator
Staff member
That's not the circuit of a periodically sampled VCO/counter combo. It's only able to acquire a monotonously increasing input signal that never decreases again because counter counts only up. Check e.g. with a square wave.

Please think it over and clarify the intended circuit function.

#### garimella

##### Full Member level 4
Hi FvM, I did not understand. This is intended function. Closed loop TF is a first order filter and the corresponding gain is evaluated as shown in the simulation results.