Calculating Input Impedance of Multiple Feedback Low Pass filter.

[sean87]

Hi all,

I am designing a filter according to this guide: http://www.cirrus.com/en/pubs/appNote/AN048Rev2.pdf

On the second step, I should calculate the imput impedance of the filter (in symbolic way):



The transfer happens to be:



So far this is my progress, I can't go any further so I call for SOS!

[Bored@Work]

On the second step, I should calculate the imput impedance of the filter.

No, you shouldn't. You should just select the minimum input impedance you would like to have. If it later turns out R1 is lower than the desired input impedance you vary C2 and C5 (start with decreasing C5) and do the calculation again, until you end up with an R1 that is greater than the desired input impedance.

[amspire]

Normally, the input impedance is not important as the input connects to an op-amp output, but you can calculate it if you need it.

BoredAtWork is completely correct. If you make sure R₁ is greater then the minimum impedance that you need, you will probably be fine.

I do remember the systematic way solving circuits using Kirchoff's Law from University days. I think that was the last time I solved a circuit using that method.

I like to understand what is going on, so here is my approach.

If you look at the filter,  the two key things the opamp is doing is:
 

• Keep the junction of R₃ and C₅ at 0v
• Draw no current from the junction of R₃ and C₅
  

So I have started the solution with the voltage across R₃ since it defines the current in C₅ and hence V_OUT.

Some times the really important thing is to know where to start getting the equation for a circuit. For example, if you ever have to get the solution to an LC filter, you start at the output voltage and work back towards the input.

[jimmc]

I think there is a bit of confusion here as to why the input impedance is important.
It is better to consider the impedance of the source from which the circuit is fed.
If this circuit is fed from a source resistance of (say) Ro then the effective value of 'R1' in the equation becomes (R1+Ro) and so the 'real' value of R1 must be reduced by Ro to maintain the calculated frequency response.
Of course if the original value of R1 is less than Ro, the filter cannot give the desired response.

As an aside, for a quick check on input impedance....
At very low frequencies all capacitors are effectively open circuit, so R4 is the only feedback path and the junction of R1, R2 & R4 is a virtual earth, thus input resistance = R1
At very high frequencies all capacitors are effectively short circuit so the junction of R1, R2 & R4 is shorted to earth by C2 , thus input resistance = R1.
For input impedance between these two extremes use a simulator such as LTSpice (free from Linear Technology)

Jim

[amspire]

Jim,

I suspect you are right in that Sean87 misunderstood the Step2 in the PDF: Determine the minimum input impedance.

What the Cirrus Logic App Note meant to say was "write down a minimum impedance that suits your circuit", and their Step 6 was making sure that R₁ was greater then this minimum impedance.

That is basically what BoredAtWork said.

You are correct about having to adjust for R_o, but if the filter gets its input from an opamp circuit, R1 will usually need to be a few KOhms at least, and R_o can be ignored.  If you were feeding a microphone directly into the filter, then you would definitely reduce R₁ by the resistive impedance of the microphone, and you would probably need to check that the reactive part of the microphone's impedance doesn't significantly change the filter's performance.

Definitely you can use LTSpice - a very good suggestion.

But often using the equations is much better, so I though I would just go and solve Sean87's question.

Using equations is way faster if you need to optimize for production - like picking the optimum capacitor values and filter specs for a result that uses all standard capacitor and resistor values, and a result that performs to spec in spite of normal component variations. You can almost do the same thing in LTSpice, but trying to optimize in Spice is very slow.

I was impressed that Sean87 was plowing through the fairly heavy fomulae of filter design, and I wanted to show that deriving  a formula for input impedance can be done, or anything else you want, can be done in a fairly quick way - with enough practice.

But you are right - there are good intuitive ways you can look at the same problem, and very often, they are all you need to do. Looking at DC and high frequency simplifications of the circuit is a really useful technique.

Richard

[sean87]

Thanks a lot guys! You helped a lot!