AN3984 Datasheet, PDF (7/46 Pages) STMicroelectronics – The purpose of this document is to provide a tool to calculate

AN3984
First-order filter design (LPF and HPF)
3
First-order filter design (LPF and HPF)
The preliminary step to obtain the coefficients for the first-order low-pass filter or high-pass
filter is to define three constants obtained from the filter parameters:
Equation 7
ω_c = 2⋅ π ⋅ f _c f _s
K = tan(ω_c 2)
α = 1+ K
In a first-order filter both the coefficients a₂ and b₂ are null.
The denominator coefficients are identical for both an LPF and an HPF designed for the
same cutoff frequency and they are computed as follows:
Equation 8
a₀ = 1
a₁
=
−
(1
−K
α
)
The numerator for an LPF can be calculated as follows:
Equation 9
b₀
=
K
α
b₁
=
K
α
The numerator for an HPF can be calculated as follows:
Equation 10
b₀
=
1
α
b₁
=
−
1
α
The coefficient used in APWorkbench can be calculated by applying these formulas:
Equation 11
Coefficient
b_{1 2}
=
(b₁ 2)
a₀
Coefficient
b₂
=
(b₂ )
a₀
Coefficient
a_{1 2}
=
(− a₁
a₀
2)
Coefficient
a₂
=
− a₂
a₀
Coefficient
b₀
2
=
(b₀ 2)
a₀
Doc ID 022240 Rev 1
7/46