Filters Notes

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General Notes

Symbols:

Sqrt[n]

Units of measure:

Filter's Magnitude Response

	Lowpass	Highpass	Bandpass	Bandstop
G A I N
FREQUENCY

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.

Recommended Resistors

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/degC	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.

Recommended Capacitors

Type	Temp. Coeff. ppm/degC	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	from	to
10	100	100000	470000
100	500	22000	100000
500	1000	6800	39000
1000	5000	2700	10000
5000	10000	1000	3300
10000	50000	560	1500
100000	500000	330	1000

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/degC.

To avoid auto-oscillations connect two 100000 pF capacitors between ground and power pins (+V, -V) of op amp IC.

Most common pinouts for op amp ICs:

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