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:

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

I calculate transfer function using quadrupole network method:

Network matrix:

And here is a transfer characteristic:

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

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: Dispersion:

Calculated data

Frequency	Hz	Average	Dispersion
Least	994177	1226203	1.486E+10
Optimal	1202954
Maximal	1485129

We se 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 – optimization is needed.

Mathcad Source.zip

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