How to linearize the Vtune vs. OSC freq

madengr said:

I did this years ago to linearize a YIG oscillator for FMCW radar. IIRC I plotted F vs Vtune (F is the dependent variable), fit a polynomial, and then used Analog Devices multipliers to generate the polynomial.

If you can get a hold of Analog Devices Nonlinear Circuits Handbook from 1976 it shows how to build multipliers, dividers, RMS and LOG detectors, etc.. with opamps.

Click to expand...

I tried this technique but I left it. As you said I plotted the Fre vs Vtune charateristic and I used the Lagrange interpollation to have a 3 degree Polynom.

My question to you madengr is how to generate this Polynom. and how to compute the bandwith of the closed loop transfert function if this VCO is used to construct a PLL ?

Dear lllxb,

I asked our Rf IC guys and their answer surprised me a bit. It looks like I gave not right advice. They do it by placing an array of varactors with different areas and switch them digitally. What we did 30 years ago is not the best way today.

Best regards,
RF-OM

The polynomial can be generated with analog multipliers such as:

**broken link removed**

The BW of these is high much higher than loop-filter bandwidth so you don't need to worry about it.

Of course this won't help you in an IC implementation. As I said though, there are ways to generate non-linear transfer functions using arrays of FETs. I have not done it but it is done. Put it this way, your FET ID is proportional to VGS^2. Your frequency is proportional to sqrt (c); I assume your tuning FET's CGS vs. Vtune is linear and that's the problem. If you take the Vtune and drive a FET, then that current is Vtune^2. Put that current through a resistor to develop a voltage which drives the tuning FET, so that would make F proportional to Vtune.

Do you really need to linearize your VCO? It's in feedback so it will lock unless your stability margin is so slim that the VCO gain change over tuning range is enough to cause ill effects.

That is overkill.

I have not worked on one in a coon's age, but it is basically an inverter op amp, with an input resitance and a feedback resistance. Then in parallel with the feedback resistance, there are more series connected Resistor-diodes. If the diodes are zener diodes, then when the op amp output gets high enough in voltage, the zener turns on and the feedback resistance is now smaller (original feedback resistor with the on-zener and 2nd resistor in parallel). A little higher in output voltage and the next zener-resistor turns on.

I have seen it done with regular junction diodes and resistive voltage dividers set up so the diode turns on when the voltage divider setpoint is reached.

Added after 2 minutes:

US Patent 4736169 looks like it has such a circuit. I am sure you can google "breakpoint linearizer" and find more info.

Added after 3 minutes:

http://www.datasheetcatalog.org/datasheets/185/177518_DS.pdf

Has a single diode linearizer op amp circuit with R3, R4, D1. You can add more breakpoints with more diode/R circuits in parallel.

Hello biff44,

May be you are right. This is not my area. But zener diode is an excellent noise generator especially with small currents as it in case when zener is in feedback. You definitely will have a problem with noise.

madengr said:

The polynomial can be generated with analog multipliers such as:

**broken link removed**

The BW of these is high much higher than loop-filter bandwidth so you don't need to worry about it.

Of course this won't help you in an IC implementation. As I said though, there are ways to generate non-linear transfer functions using arrays of FETs. I have not done it but it is done. Put it this way, your FET ID is proportional to VGS^2. Your frequency is proportional to sqrt (c); I assume your tuning FET's CGS vs. Vtune is linear and that's the problem. If you take the Vtune and drive a FET, then that current is Vtune^2. Put that current through a resistor to develop a voltage which drives the tuning FET, so that would make F proportional to Vtune.

Do you really need to linearize your VCO? It's in feedback so it will lock unless your stability margin is so slim that the VCO gain change over tuning range is enough to cause ill effects.

Click to expand...

That looks a good idea. But will it affect the Noise performance?

Sure, but how much is unknown. A bipolar would be better than a FET for noise. But a single FET may be better than a whole op-amp. You'll just have to try it.

RF-OM said:

Dear lllxb,

I asked our Rf IC guys and their answer surprised me a bit. It looks like I gave not right advice. They do it by placing an array of varactors with different areas and switch them digitally. What we did 30 years ago is not the best way today.

Best regards,
RF-OM

Click to expand...

Dear RF-OM

I need to get a linear Freq vs. Vtune. Ur idea here looks lile some digital tuning.

Okay, I got it. I thought you are looking for the best solution. If I remember right we did it with diodes array and biased eacn diode independently. This way allows to get practically any curve. I just not sure that it is good way for today.

Best regards,
RF-OM

RF-OM said:

Okay, I got it. I thought you are looking for the best solution. If I remember right we did it with diodes array and biased eacn diode independently. This way allows to get practically any curve. I just not sure that it is good way for today.

Best regards,
RF-OM

Click to expand...

How do u bias them? will it affect the VCO phase noise?

It can be done with potentiometers or with resistors connected as voltage dividers. Usually regular detector diodes do not introduce significant noise with small current, but it is better to check any particular diode before use it. You may see similar schematic for quadratic detector. This is the detector circuit that have output voltage proportional the square of input signal amplitude. This kind of detector often used in measuring devices which measure power because voltage squared is actually the power for given resistance. Although it is not very wide known circuit as amplifier or mixer you may find it. I also used such a circuits for analog computers (they were very popular before digital machine). There we used such method of forming arbitrary curves with OP amps built on tubes.

Best regards,
RF-OM