Filter Specifications
Approximation Type
Response Type
Order N
4
Cutoff Frequency fc
1000 MHz
Passband Ripple Rp
0.5 dB
Stopband Attenuation As
40 dB
Prototype Element Values
—
Order N
— MHz
Cutoff fc
— dB
Passband Ripple
— MHz
-40dB Frequency
—
LC Element Count
—
Filter Type
— dB
|S11| at fc
— ns
Passband Group Delay
LC Ladder Circuit (Prototype)
Frequency Response |S21| and |S11| [dB]
Group Delay [ns]
Theory Notes
Butterworth transfer function:
$$|H(j\Omega)|^2 = \frac{1}{1+\Omega^{2N}}$$
Chebyshev Type I:
$$|H(j\Omega)|^2 = \frac{1}{1+\varepsilon^2 T_N^2(\Omega)}$$
Group delay:
$$\tau(\omega) = -\frac{d\phi(\omega)}{d\omega}$$
Frequency transformation (LPF→BPF): $s \to \frac{s^2 + \omega_0^2}{s \cdot BW}$
Practical Note: If passband ripple is acceptable, choosing Chebyshev achieves a steeper transition than Butterworth by effectively one order. Elliptic filters offer even steeper rolloff but have ripple in both passband and stopband. In microwave design, lumped LC elements are replaced by distributed elements (microstrip lines), but prototype element values remain the same.