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Figure 16-13. First-Order Inverting Low-Pass Filter: A(s) 1 1 R C S A(s) 1 R C S

This document describes a first-order inverting low-pass filter circuit. It contains two transfer functions that generate a 180 degree phase shift from input to output. To dimension the circuit, specify the corner frequency, dc gain, and capacitor, then solve for the resistor values using the equations provided. All first-order filter types have an a1 coefficient of 1, but for higher orders the coefficient is different due to differing corner frequencies between stages.

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33 views1 page

Figure 16-13. First-Order Inverting Low-Pass Filter: A(s) 1 1 R C S A(s) 1 R C S

This document describes a first-order inverting low-pass filter circuit. It contains two transfer functions that generate a 180 degree phase shift from input to output. To dimension the circuit, specify the corner frequency, dc gain, and capacitor, then solve for the resistor values using the equations provided. All first-order filter types have an a1 coefficient of 1, but for higher orders the coefficient is different due to differing corner frequencies between stages.

Uploaded by

lecuellarq85gmailcom
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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C1

R1 R2
VIN
VOUT

Figure 1613. First-Order Inverting Low-Pass Filter

The transfer functions of the circuits are:


R R
1 ) R2 * R2
A(s) + 3 and A(s) + 1

1 ) w cR 1C 1s 1 ) w cR 2C 1s

The negative sign indicates that the inverting amplifier generates a 180 phase shift from
the filter input to the output.

The coefficient comparison between the two transfer functions and Equation 163 yields:

R2 and R2
A0 + 1 ) A0 + *
R3 R1

a 1 + w cR 1C 1 and a 1 + w cR 2C 1

To dimension the circuit, specify the corner frequency (fC), the dc gain (A0), and capacitor
C1, and then solve for resistors R1 and R2:
a1 and a1
R1 + R2 +
2pf cC 1 2pf cC 1

R2
R 2 + R 3A 0 * 1 and R1 + *
A0

The coefficient a1 is taken from one of the coefficient tables, Tables 164 through 1610
in Section 16.9.

Note, that all filter types are identical in their first order and a1 = 1. For higher filter orders,
however, a11 because the corner frequency of the first-order stage is different from the
corner frequency of the overall filter.

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