Notes on Filters

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General Notes


  • pi represent the Greek P value (3.14159265…)
  • Fc represent the cutting frequency.
  • Sqrt[n] represent the Square Root of number n (eg. Sqrt[2]=1.414213…)

Units of measure

  • Resistance [Ohm]
  • Capacity [F]
  • Frequency [Hz]

Filter’s Magnitude Response

Highpass Bandpass Bandstop
GAIN Lowpass Magnitude Response Highpass Magnitude Response Bandpass Magnitude Response

N-Order Filter

To make a n-order filter (where n>2) you have to connect first order and second order filters in cascade (series).If n is even (4,6,8,10,…) use n/2 second order filters.If n is odd (3,5,7,9,…) use 1 first order filter and (n-1)/2 second order filters.

The attenuation for n-order filter is 6·n dB/octave.

Resistors are generally sized between 1Kohm and 100Kohm. A more general rule is that any resistor value in the op amp RC network should at least ten times the output resistance of the op amp and less than one-tenth the input resistance of the op amp.

Type Temp. Coeff. (ppm/°C) Stnd.Tolerances (%) Comments
Metal film -25 -> 100 1 low cost; most widely used
Cermet film 200 0.5,1 larger, costlier than metal film
Carbon film -200 -> -500 2,5,10,20 low cost; negative temp.coeff.

Carbon film resistors are included because their negative temperature coefficient can be used to advantage to minimize the passive sensitivity of a circuit (if the capacitors have a positive temperature coefficient).Carbon composition resistors are not included because of their high temperature coefficient and high noise level. Carbon composition variable resistors are also not recommended.

Type Temp. Coeff. (ppm/°C) Comments
NPO ceramic 0 +/- 30 most popular for active filters
Film: MPC 0 +/- 50 metallized polycarbonate
Film: Polystyrene -120 larger than MPC; melts at low temp.
Mica -200 … + 200 larger, costlier than NPO

Predictable negative temperature coefficient of polystyrene capacitors can be used to advantage with metal film or cermet film resistors to minimize passive sensitivity.Standard tolerances all of these capacitors include 1,2,5 and 10%.

Fc = Frequency Cut Capacity in pF
from to
10 100
100 500
500 1000
1000 5000
5000 10000
10000 50000
100000 500000

Operational amplifier

Unity-gain bandwidth characteristics

A manufacturer’s data book will usually include the unity-gain bandwidth in the op amp’s electrical characteristics. Often, a minimum, typical and maximum value will be given, from which the GBW tolerance can be estimated:

tol = ((TYP - MIN)/TYP)x 100% 

The range of op amp tolerances is wide; from around 15% to about 50%, with the mean approximately 30%. The GBW temperature coefficient must be estimated from a graph of (normalized) unity gain bandwidth versus free air temperature. This graph is not always provided. Typical coefficient values might be 1000 to 7000 ppm/°C.

To avoid auto-oscillations connect two 100 nF capacitors between ground and power pins (+V, -V) of op amp IC.


Most common pinouts for op amp ICs




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