Current source transfer function

Thread Starter

leech10

Joined Jun 7, 2017
18
Hello


I created op amp MOSFET current source. It had oscillations as per picture, so RC circuit was was added and problem was resolved. What I am wondering is a transfer function of it and how to treat it. Controller works as an error amplifier, but is it the simplest form of proportional controller? And after addition of the capacitor, does it make this circuit simple PI controller? If so how can I write transfer function of it. For example if I Op Amp is PI controller Gc(B) what the Kp gain will be? And I dont know how to describe transfer function of Mosfet Gp(B).

Could someone please help me with this.
 

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Thread Starter

leech10

Joined Jun 7, 2017
18
Hi

Someone posted comment but it was removed however there was important info. I treated this circuit as error amp which may be wrong as RL is a static value so there is no error to compensate. Now I see that my way of thinking on this case might have been wrong. Anyway I still wonder how to solve itransfer functuoion of it. As there is no error to compensate for DC it acts as buffer/Voltage follower. Vout/Vin = 1. And for AC(oscillations) it has RC loop. But I'm not sure if we can treat it as Integrating part of the system as in PI.
 

OBW0549

Joined Mar 2, 2015
3,566
Controller works as an error amplifier, but is it the simplest form of proportional controller? And after addition of the capacitor, does it make this circuit simple PI controller?
No. The capacitor has absolutely nothing to do with making the circuit a PI controller.

The operation of this circuit is really very simple: op amp U1 drives M1's gate to maintain the voltage on the top end of of the 4.7Ω resistor the same as the incoming control voltage. The 330Ω resistor isolates M1's gate from the op amp's output, helping to prevent VHF/UHF oscillations in M1. The 1 nF capacitor together with the 10kΩ resistor act to stabilize against low-frequency oscillations caused by loop instability.

As for the transfer function of the circuit (Id of M1 versus the control voltage), it is simply a constant with a value of (1/4.7) amps/volt at DC and low frequencies, rolling off at -20 db/decade above a pole whose frequency is determined by the 1 nF capacitor and the 10kΩ resistor (about 15.9 kHz).

And that's about all there is to it.

EDIT: this Linear Technology app note gives a more thorough treatment of instability in op amp feedback loops and techniques for mitigating it.
 
Last edited:

drc_567

Joined Dec 29, 2008
1,156
... tried to run your circuit as LTspice simulation. ... Not getting any oscillation.
You may be dealing with small value parameters ... parasitic values.
... The LT1013 is suggested as being a replacement for the LM358.
 

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MrAl

Joined Jun 17, 2014
11,342
Hello


I created op amp MOSFET current source. It had oscillations as per picture, so RC circuit was was added and problem was resolved. What I am wondering is a transfer function of it and how to treat it. Controller works as an error amplifier, but is it the simplest form of proportional controller? And after addition of the capacitor, does it make this circuit simple PI controller? If so how can I write transfer function of it. For example if I Op Amp is PI controller Gc(B) what the Kp gain will be? And I dont know how to describe transfer function of Mosfet Gp(B).

Could someone please help me with this.
Hi,

Actually both circuits create an integral controller, the first though does not have the proper (complex) loop gain while the second does. This is harder to model because the op amp internal compensation has something to do with the integration too and if the loop factor is not right it will still oscillate, and that's why the cap helps because it brings the poles to the left hand plane and that means it's stable. This will vary with the choice of op amp though, and also may vary with the type of load if it is not pure resistive.

So your circuit, especially the second one, is really like this:
1. Subtractor
2. Integrator
3. Driver
4. Negative feedback

The subtractor is the error amp, the integrator is the capacitor combined with the op amp, the driver is the op amp output stage and resistor and MOSFET.

The gain of the MOSFET in this circuit is considered unity, but there is some capacitance associated with the gate source and gate drain that could cause instability too without that added cap.

Integral control is what makes the output very very nearly equal to the control reference voltage in the steady state solution. Before it reaches steady state however there could still be what looks like ringing, and the amount of ringing and frequency depends on the value of the cap. IN applications like this there is also usually a lot of attention to how much it rings and what the max peak is as well as the settling time, and also sometimes how well it follows various input test signals like ramp and sometimes exponential.
 
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