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ZHCSOD5L April 2000 – August 2023 THS4130 , THS4131

PRODUCTION DATA

9.2.2 Detailed Design Procedure

Figure 9-5 shows a multiple-feedback (MFB) low-pass filter. The transfer function for this filter circuit is:

H_{d} (f) = [\frac{K}{- {[\frac{f}{F S F \times f c}]}^{2} + \frac{1}{Q} \frac{j f}{F S F \times f c} + 1}] \times [\frac{\frac{R t}{2 R 4 + R t}}{1 + \frac{j 2 π f R 4 R t C 3}{2 R 4 + R t}}]

Equation 4.

w h e r e K = \frac{R 2}{R 1}, F S F \times f c = \frac{1}{2 π \sqrt{2 \times R 2 R 3 C 1 C 2}}, a n d Q = \frac{\sqrt{2 \times R 2 R 3 C 1 C 2}}{R 3 C 1 + R 2 C 1 + K R 3 C 1}

K sets the pass-band gain, fc is the cutoff frequency for the filter, FSF is a frequency scaling factor, and Q is the quality factor.

Equation 5.

F S F = \sqrt{{R e}^{2} + {|I m|}^{2}} a n d Q = \frac{\sqrt{{R e}^{2} + {|I m|}^{2}}}{2 R e}

where Re is the real part and Im is the imaginary part of the complex pole pair. Setting R2 = R, R3 = mR, C1 = C, and C2 = nC results in:

Equation 6.

F S F \times f c = \frac{1}{2 π R c \sqrt{2 \times m n}} a n d Q = \frac{\sqrt{2 \times m n}}{1 + m (1 + K)}

Start by determining the ratios, m and n, required for the gain and Q of the filter type being designed, then select C and calculate R for the desired fc.