Differencial Input/Output Biquad Band-Pass Filter

Differencial Input/Output Biquad Band-Pass Filter

$T_\mathrm{BP}(s) &=& h \frac{\displaystyle\frac{\omega}{Q} s}{ s^2 + \displaystyle\frac{\omega}{Q} s + \omega^2$

Japanese edition is here.

General discriptions

First-order pairs Biquad band-pass filters with differential inputs and outputs for building blocks of active filters.

Schematics

fig.1 Schematics for simulation (f_C = 10 kHz, Q = 5, h = 2)

The inputs are not high-impedance and must be driven from a low-impedance signal source, such as the op-amp output.
It can also be used as an unbalanced input by removing R3, C3, and R4 and grounding the non-inverting input pin of U1.
By swapping C2 and R6, the outputs of U2 and U3 can be changed to a second-order low-pass filter with differential outputs.

diff-bq-bpf-1.0.zip [zip, 3 kB] — the schematic file for the LTspice XVII.

Transfer functions

$\mathrm{let}&& R_3 = R_1, \quad \frac{1}{R_4} = \frac{1}{R_2} + \frac{1}{R_8}, \quad R_6 = R_5\\ T_\mathrm{BP-}(s) &=& - \frac{R_2}{R_1} \frac{\displaystyle\frac{1}{C_1 R_2} s}{ s^2 + \displaystyle\frac{1}{C_1 R_2} s + \displaystyle\frac{1}{C_1 C_2 R_7 R_8}},\quad T_\mathrm{BP+}(s) = - T_\mathrm{BP-}(s)\\ T_\mathrm{LP-}(s) &=& - \frac{R_2}{R_1} \frac{\displaystyle\frac{1}{C_1 C_2 R_2 R_7}}{ s^2 + \displaystyle\frac{1}{C_1 R_2} s + \displaystyle\frac{1}{C_1 C_2 R_7 R_8}}$

Simulation results of the example

fig.2 Frequency V.S Amplitude · Group delay (an example)(f_C = 10 kHz, Q = 5, h = 2)

fig.3 Transcient response (f_C = 10 kHz, Q = 5, h = 2, f_s = 10 kHz, f_cm = 1 kHz)

References

"Electronic filter design handbook", B. Williams, Fred J. Taylor, McGraw-Hill

External links

LTspice

General discriptions

Schematics

Transfer functions

Simulation results of the example

See Also

References

External links