Sallen Key Circuit for High Pass Bessel
The applet on this page uses 2nd and 3rd order Sallen Key circuits to construct HP Bessel Filters with orders 2 to 8.
Even order filters 2, 4, 6, 8 can be constructed from 1, 2,
3, 4 second order sections. Odd order filters 5, 7 can
be constructed from 1 third order and 1, 2 second
The applet calculates normalized and denormalized components
and illustrates the magnitude and phase error introduced when any of the components are out by ± 20%.
The Circuits used are shown above.
Normalized circuit components are calculated by first calculating
LP normalized values then replacing each resistor with resistance R
ohms with a capacitor
= 1/R Farads and each capacitor of C Farads with a resistor of
In the applet below, the filter shown is determined by Fn which is
set by scrollbar (0). Fn = 1 to 7 shows filters with orders 2 to 8.
The normalized component values are shown by the green text on the applet.
The denormalized component values are calculated from the normalized
values, the 3dB frequency set by scrollbars(38, 39 and 40) and
the impedance scaling factor set by scrollbars(41 and 42).
Denormalized component values are shown by the yellow text on the
Scrollbars 11 to 30 are used to show the effect that inaccuracies
in the component values can have on the circuit transfer function.
The green text at the top show which component are affected by
which scrollbar. eg R1 is changed by scrollbar (11) and C1 by
scrollbar(21). The % change from the correct value is shown for each component.
Scrollbars (45 to 48) are used to change the gain of the
error and T/F phase and magnitude.
The Image below shows a 8th order filter (Fn = 7) implemented
with 3 sections and 3 opamps(8 resistors and
8 capacitors). Normalized
components are shown in green at the top and denormalized
components are shown in yellow at the bottom. In this case,
the 3dB frequency is 200Hz and the Impedance scaling factor
Pink and Cyan plots show the magnitude and phase error
introduced when the capacitor C2 in section 3 is 20%
less than its correct value. 20% change is shown in the
normalized components at the top but does not affect the
denormalized components at the bottom.
Numerical values of the errors can be seen at the bottom by using scrollbar 43 to move the white line.
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COPYRIGHT © 2010 Cuthbert Nyack.