What is the correct order in the insertion loss design of a microwave filter?

Choose response, find order N, take LP prototype g-values, scale/transform, implement

Fabricate, simulate, choose response, find N

Scale values, choose response, find N, read prototype

Implement with stubs, then specify cut-off

In the LP-to-HP transformation, what does the series L of the prototype become?

Series capacitor C = 1/(ωc R0 g)

Series inductor of the same value

For a Butterworth N = 3 HPF (g = 1, 2, 1), fc = 2 GHz, R0 = 50 Ω, which element values result?

C1 = C3 = 1.592 pF, L2 = 1.989 nH

C1 = C3 = 1.989 nF, L2 = 1.592 pF

C1 = C3 = 7.96 pF, L2 = 1.59 nH

C1 = C3 = 1.592 nH, L2 = 1.989 pF

How is the shunt inductor L2 realised in microstrip, and what is a drawback?

Short-circuited stub (via to ground); a spurious stopband appears near where the stub is λ/2

Open-circuited stub; no drawback

Gap capacitor; narrow bandwidth

2074 Bhadra · 6+4 marks

Filter design steps and microstrip HPF

Short answer

Design uses insertion loss method: specify response, choose Butterworth/Chebyshev, find order, prototype g values, scale/transform to HPF, implement with stubs/gaps. Example N=3 Butterworth HPF at 2 GHz, 50 Ω: series capacitors 1.59 pF, shunt inductor 1.99 nH realised as gap/interdigital capacitors and shorted stub 6.19 mm.

Explain in detail the designing steps of microwave filters. Illustrate an example of passive HPF using microstrips.

Microwave filters are designed mainly by the insertion loss method: a low-pass prototype is synthesised for the required response, then scaled, transformed and built with transmission-line elements.

Design steps

Specifications: type (LP/HP/BP/BS), cut-off fc, ripple, stopband attenuation, R0, size/substrate.
Choose the response: Butterworth PLR = 1 + (ω/ωc)^(2N) (flat), Chebyshev PLR = 1 + k²TN²(ω/ωc) (sharper, rippled), or linear phase.
Find the order N from the stopband attenuation.
Low-pass prototype values g1…gN+1 from tables (R0 = 1 Ω, ωc = 1).
Scaling and transformation:

LPF: L = gR0/ωc,  C = g/(R0ωc)
HPF: series C = 1/(ωc·R0·g),  shunt L = R0/(ωc·g)
BPF/BSF: use ω0 and fractional bandwidth Δ

Implementation: Richards' transformation (L → short stub, C → open stub), Kuroda identities (convert series stubs to shunt stubs), stepped-impedance lines, or coupled lines for BPF.
Simulate, optimise, fabricate and measure.

Example: passive HPF using microstrip

Specs assumed: fc = 2 GHz, R0 = 50 Ω, Butterworth N = 3 (g1 = 1, g2 = 2, g3 = 1). The LP prototype series L – shunt C – series L becomes series C – shunt L – series C:

C1 = C3 = 1/(2π×2×10⁹ × 50 × 1) = 1.592 pF
L2      = 50/(2π×2×10⁹ × 2)     = 1.989 nH

Microstrip realisation (εr = 4.2, h = 1.58 mm assumed):

Series capacitors C1, C3: gap-coupled or interdigital capacitors in the 50 Ω line (width 3.13 mm), sized to give 1.59 pF.
Shunt inductor L2: short-circuited stub (via hole to ground). For a 50 Ω stub, Z·tan(βl) = ωcL2 = 25 Ω → βl = 26.57°, length ≈ 6.19 mm at 2 GHz.

  50Ω   C1  ||     C3  ||   50Ω
 =======|| |===+===|| |=======
          (gap) |  (gap)
                | L2: shorted
                | stub 6.19 mm
               _|_
              (via) ground

The response gives 3 dB loss at 2 GHz and about 18 dB at 1 GHz. Because a stub is resonant, a spurious stopband appears near the frequency where the stub is λ/2; this is checked in simulation.

✓ Answer checked by Claude Opus 5.5 (high effort)

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Filter design steps and microstrip HPF

Design steps

Example: passive HPF using microstrip

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