# How to simulate the exponential growth op-amp?

According to Wikipedia, the following is the exponential output operational amplifier.

I would like to test this out in a simulated environment and see how this functions. For example give a sine wave as the input and observe the resulting output signal.

But I do not have any prior knowledge about simulating electrical circuits. Could somebody help me out here by suggesting a way to get started with this ? Thanks!

• Are you going to use simulink or why did you add that tag? – pipe Dec 17 '18 at 8:30
• I am open to using any simulating platform for doing this. I was not sure which would be the best. – 256ABC Dec 17 '18 at 8:34
• Your first step should be to think about how this circuit works. If the diode confuses you then make it a resistor and think how that would work. This circuit applies the input voltage directly to the diode, then the current through the diode is converted to a voltage by resistor R. Think about the relation between a voltage across a diode and the resulting current through it. – Bimpelrekkie Dec 17 '18 at 8:41
• If you have no experience with a circuit simulator, there's a chance you'll use it the wrong way and you will get weird results. If you have not thought about what the result should be you could think that that weird result was the actual behavior of the circuit. That's why you should only use the simulator to confirm what you think the behavior should be. – Bimpelrekkie Dec 17 '18 at 8:45
• Why consider other circuits? What's wrong with this one? I think you do not realize that an exponential relation will only be valid over a very small range of input voltage as a change at the input results in an exponential change at the output. The challenge is to keep the input voltage within that range. – Bimpelrekkie Dec 17 '18 at 9:14

The circuit topology you are showing is an exponential amplifier (an antilog), where the output voltage is proportional to the exponent of the input voltage.

How to simulate it? and in Simulink (as per the tags), by building a model. That is where the annoyance comes from. An antilog amplifier works because of the exponential characteristics of a PN junction and thus to simulate this you must model this characteristic.

This is where the specifics of the simulation packages becomes important. The modeling of the diode can be split into 3

1. Ideal model: This will model the diode as the textbook conduction/blocking
2. Ron model: A slight improvement but treating the diode characteristics during conduction as linear. Valid for power calcs.
3. Exponential model: Be it SPICE or MAST or SIMSCAPE.

For simulink, the base Simscape's electrical domain only offers #2. The Electronics module does offer an exponential model and this is key as this is the behaviour such an amplifier relies on.

The current equation of a diode can be summaries as $$\ I_f = I_{o} \cdot e^{ \frac{V_{in}}{V_t}} \$$

Assuming ideal opamp and thus If must be the current flowing through the feedback resistor

$$\I = I_f = \frac{V_- - V_o}{R_f} = \frac{-V_o}{R_f} \$$

$$\V_o = -I_o R_{fb} e^{ \frac{V_{in}}{V_t}} \$$

If you really want to model such a circuit, look into SPICE-based simulators as you need the characteristics of the diode.

Try this

simulate this circuit – Schematic created using CircuitLab