Design a circuit from input-output characteristics

[fourierpwn]

Hi all,

I am trying to understand what is happening in the image below and how to design a circuit based on these characteristics. Any help would be appreciated.

There is no example circuit for this and very little info given.

[fourierpwn]

My main question is what is meant by V1, 2V1, 3V1 etc. I feel one needs to think in terms of a circuit whose transfer function is a sinusoid with time-period dependent on V1.

A circuit whose input-output relation is,
 
Vout = V0*Sin(2*pi*Vin/V1)

I could be wrong. 

[Ian.M]

Replace the phrase 'sinusoid with time-period dependent on V1' with 'a sinusoidal function of V1' and you've nearly got it, except for an extra factor of two you shouldn't have, so the formula is:

  Vout=V0*Sin(pi*Vin/V1)

Also the output is only specified over the Vin range 0 to 4*V1, which is important when you need to design a real-world implementation.

A simulation based on the mathematical transfer function is trivial (LTspice sim attached), but a real world circuit without using digital processing would be a *LOT* harder.

Lets suppose the input is a linear ramp ovwer the range 0 to 10V in time 4T.  The desired output is a sinewave of period T.One possible approach would be to convert the linear ramp to a triangle wave then apply that to a sine shaper circuit.  The conversion to a triangle wave would be made by inverting it, and appliying the original and the inverted voltage through various weighting resistors and clamps to a summing amplifier.  The first section is just proportional to Vin, the next adds a component of -2*Vin above V1/2 to give the down slope needed between V1/2 and 3V1/2 etc.   Then its just a very carefully biassed diode and resistor network that provides the sine shaping and an output buffer amp.

An alternative approach would involve a sinewave generator at a frequency a couple of orders of magnitude higher than the maximum input frequency, a circuit that generates a pulse on every other rising zero crossing, feeding  a linear voltage controlled delay, that outputs a pulse to a sample and hold circuit to pick off the required output level from the sinewave.   

I wouldn't build either on a bet, as an ADC  addressing a lookup ROM feeding a DAC would be far more practical, and if the resolution and update rate is low enough, it could all be done in a small MCU.

[fourierpwn]

..so the formula is:

  Vout=V0*Sin(pi*Vin/V1)

You're right. My mistake.

You presented two interesting approaches. However, the problem states that particular MOSFET models are to be used and there is no mention of what other devices are acceptable so I am not sure if the use of op amps is allowed or not.

I'll have a bit more of a think about it.

Thanks for your response Ian.M