2nd order low pass fillter

Discussion in 'Homework Help' started by Jaywin, Apr 22, 2008.

1. Jaywin Thread Starter New Member

Apr 20, 2008
9
0
For the 2nd order low pass filter
is the input impedence calculate like this:
Zin = 1/jwC1 + R2||(R2+1/jwC2)
if freq-> inf then the Zin is just R1||R2.
Am i correct? That is wave generated using Pspice.^^  2. Caveman Senior Member

Apr 15, 2008
471
1
Actually as f->infinity. Zin = R1. Assuming perfect opamp of course.

3. Caveman Senior Member

Apr 15, 2008
471
1
Otherwise, you just analyze the circuit to get the voltage at the node between R1 and R2, Va.

Zin = (Vin-Va)/R1.

There might be an easier way, but I don't know it.

4. Jaywin Thread Starter New Member

Apr 20, 2008
9
0
Zin = (Vin-Va)/R1?

(Vin-Va)/R1 isn't we wil obtain current? by the way, Va is same as Vc1 right?
Actually, the problem is to fulfill the specification which our
Zin >= 10kOhm
So if i put the R1 = 10kohm is also satisfy the specification right?

Zin = 1/jwC1 + R2||(R2+1/jwC2) is wrong?

5. Caveman Senior Member

Apr 15, 2008
471
1
Whoops,

Zin = R * Vin/(Vin-Va)

But yeah, R1 =10k should solve it, I think.
I frankly haven't had a chance to check your Zin since it is fairly complex to quickly calculate. I might look at it tonight.

6. The Electrician AAC Fanatic!

Oct 9, 2007
2,720
496
Is the input impedance your only specification? Don't you also have to meet a frequency response spec?

Go back to the Spice plot of Zin in your first post, and look carefully at the region between 3000 Hz and 4000 Hz. This may be a trick question.

If you make R1 = 10k, you also might want to make R2 = 10k, and make C1 and C2 bigger to meet the frequency response spec.

But if you do that, plot Zin at about 7000 Hz and look carefully at its behavior.

I think Zin has a second order numerator.

7. Jaywin Thread Starter New Member

Apr 20, 2008
9
0
The cutoff frequency is given f0 = 1kHz
If change the R then C also have to change also using f0 = 1/2paiRC
which RC = 159.15us right?
Why have to observe certian frequency to know the Zin whether meet the
>= 10k specificatin?
Is it just look at the red-circled region if it is >=10k then we meet the specification. Am i right?

R1=R2=10k R1= R2=20k 8. The Electrician AAC Fanatic!

Oct 9, 2007
2,720
496
Adjust your plot so that the maximum vertical axis magnitude is 25k instead of 300k or 500k.

9. Caveman Senior Member

Apr 15, 2008
471
1
Man, this is nasty, but here goes:

Zin = R1/(1-H*(1+jwC2*R2)/G)

In this case H is the transfer function of the 2-pole filter. Look at wikipedia.
G is the DC gain = (3.5k + 6k)/3.5k.

That's as far as I got.