Hi, everyone

I am completely stuck with this question and the assignment is due on Wednesday. I am studying Electrical Circuits at Curtin University as part of my Mechatronic Engineering course and need help with Op-Amps.

Q1.The op Amp in the following circuit is supposed to be ideal. There is no initial energy stored in the capacitors.

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• Find the expression for the transfer function:

H(s) = Vout(s)/Vin(s)

• Let R1 = R2 = 1 kΩ, R3 = 500 kΩ, R4 = 270 kΩ and C1 = C2 = 316 pF, plot the amplitude of H(j2πf) with respect to the frequency f. What could we say about this circuit?

• If Vin(t) = 100cos(1000*pi*t) mV; find and plot the expression of Vout.

• ZL in the circuit is an AC motor, which it can be modulated by a resistor Rm = 10Ω in series with an inductor Lm = 500mH, (i.e. ZL = Rm + j w Lm ) .

• Calculate the total power transferred to ZL.

• Find the power developed by Vin. Comment the results obtained in last two questions.

• The power supply of the op Amp is Vcc = 10 V. If the amplitude of Vin has been increased by a factor ten, replot Vout.

• Using passive RLC circuits (in series and in parallel), find two equivalent circuits to H(s).

I have looked everywhere for explanations on how to get the transfer function but cant find anything useful. Our lecture has not covered the topic yet and i cant afford the textbook. Could you please help me out.

Thanks in advance,

Will

 

Do you know how to derive the equation for the output for an inverting amplifier for example? If yes, its the same procedure but use the capacitors as an impedance Xc=1/(jωC). Finally, rearrange the equation to get Vout/Vin on one side and something else on the other side. Vout/Vin is the transfer function.

 

Two words:

Sallen-Key.

 

Two more words:

Low-pass.

 

Hi thanks for your replies. I realise that it is a low pass Sallen-Key circuit but I still cant figure out the transfer function. I have been using nodal and substituting the equations so that i end up with Vout/Vin. This is the equation that i get:

Vout/Vin = C1.(R3+R4).C2/(R4.C2.C1+R4.C1.R2+C1.R1.R4+R4.R2.R1-R1.C2.R3)

Does this look right too you? If so, how do i convert this to the s domain?

Thanks,

Will

 

You don't "convert" it to the s domain. It should have been in the s domain all along as you were figuring out the transfer function.

Have a look at:

http://en.wikipedia.org/wiki/Sallen_key

 

Im not sure about this,but isnt H(s) like this:
R1=R2=R , C1=C2=C
H(s)= G/((sRC)^2+s(3-G)RC+1)
(3-G)RC=1.414 (from butterworth table)

 

Hey with regards to that question - there's two main ways I know of to derive the Transfer function, use one or both of KCL/KVL to get Vout in terms of Vin plus one node voltage/mesh current using the fact that Vn = Vp for our ideal opamp, then apply Cramer's rule. Borrow the textbook if you need help with this, then check the butterworth filter circuit and adjust for the sallen key.
For the second way look up sallen key low pass filter and you'll find lots of results - of particular interest to you will be the Texas Instruments pdf about designing sallen key filters but you'll need to learn about gain and quality factor to have much hope of understanding it.

These assignments are pretty terrible considering what they teach us - not much but they can be done, just requires a lot of individual learning. If you have any ideas on the other two questions let me know.