Electric arc simulator

I want to design an electric arc simulator(electronic load) .A sub circuit of this involves the design of a trans conductance amplifier with an IGBT. I do not want an OP-Amp based trans conductance based circuit,i'm very specific on using an IGBT for the transconductance circuit because i require a current of the order of 10 Amps.

The arc simulator circuit essentially consists of multiplier ,integrator and the trans conductance circuit -i.e with the voltage as input i will require output as current.This output is to be given back to the multiplier,which then multiplies the final voltage and current.
MY AIM is to design a circuit which gives me static V-I characteristics with negative resistance slope.
Please assist me on the same.Looking forward for valuable suggestions on how to go about on the same.

You must give some constraints for input and outputs.

V,I Z,ESR or gm, Ac,DC, load di/dt and arc V, f , gap etc.

All transistors have negative VI slope on CE or CD designs.