Filter output dependency on tolerance of elements

Sometimes we need to project simple filter with particular characteristics. We usually take calculations with ideal parameters and don’t look on tolerances of them. Let us see how simple filter output depends on its elements tolerances.

For this let’s choose simple filter circuit:

image002.jpg

We are going to calculate filter response characteristics. The band pass frequency is taken on 0.707 level of response. We will see how this frequency depends on electronic elements tolerances. I will model elements with tolerances ±10%.

I calculate transfer function using quadrupole network method:

image004.gif

Network matrix:

image006.gif

And here is a transfer characteristic:

image008.gif

Bellow you see marginal characteristics, when element values are +10% and -10%

image009.jpg

HH(w) – ideal parameters 0 deviation, HHH(w) – deviation -10%, o H(w) – +10%.

Wee see that characteristic varies in pretty wide range. If wee need to calculate band pass frequency, we need to calculate average and dispersion.

Average:

image011.gif

Dispersion:

image013.gif

Calculated data

Frequency

Hz

Average

Dispersion

Least

994177

1226203

1.486E+10

Optimal

1202954

Maximal

1485129

We see if element parameters deviation limits are ±10%, then frequency can vary from 994177Hz to 1485129Hz  the range is 490952Hz. As you see this is quit little Accuracy.

So if you need better tolerance, you need to select proper elements. And remember that not all electronic elements give the same impact in overall tolerance. To evaluate this an optimization is needed.

Mathcad Source.zip

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.