cannibol_90
Member level 5
Hi,
I am trying to model my circuit response. The frequency response and its equivalent circuit model is shown in the figures below.
At the S21 dip (transmission zero - stop-band), the susceptance of the equivalent circuit = 0. Hence,
Ys cot (θ) - 1/(ω0 Ls) = 0
θ = electrical length of the stub, ω0 = Frequency at S21 dip. Ys = characteristic admittance of SC stub.
and at S11 dip (reflection zero - pass-band), the reactance of the equivalent circuit = 0. Hence,
(Zs ωp Ls tanθ)/(ωp Ls + Zs tanθ) = 0
This indicates that tanθ = 0. So, θ= pi, 2pi, 3pi, ...
At θ = pi, the SC stub produces a pass-band, and since θ=βl; β=ω/Vp, Vp= phase velocity:
θ=pi=(2pifp/Vp)lsc; fp= pass-band frequency, λg = guided wavelength, lsc = short circuited stub length. This gives lsc,
lsc = Vp/(2 fp) = λg/2
This gives lsc = 16.6mm for a pass-band frequency of 4.92 GHz.
Also, at 3-dB cutoff frequency (ωc), the susceptance of the equivalent circuit = susceptance of a low-pass filter prototype with one pole. Hence,
Ys cotθ + 1/(ωc Ls) = 1/100 ; ωc = 3-dB cut-off frequency.
So, we have three equations,
Ys cot (θ) - 1/(ω0 Ls) = 0 -> (1)
(Zs ωp Ls tanθ)/(ωp Ls + Zs tanθ) = 0 -> (2) or Ys cot (θ) - 1/(ω0 Ls) = ∞
Ys cotθ + 1/(ωc Ls) = 1/100. -> (3)
with lsc = 16.6mm at θ = pi.
Now, can anyone help me solve these equations to deduce the values of Zs, Ls.
Please help!
I am trying to model my circuit response. The frequency response and its equivalent circuit model is shown in the figures below.
At the S21 dip (transmission zero - stop-band), the susceptance of the equivalent circuit = 0. Hence,
Ys cot (θ) - 1/(ω0 Ls) = 0
θ = electrical length of the stub, ω0 = Frequency at S21 dip. Ys = characteristic admittance of SC stub.
and at S11 dip (reflection zero - pass-band), the reactance of the equivalent circuit = 0. Hence,
(Zs ωp Ls tanθ)/(ωp Ls + Zs tanθ) = 0
This indicates that tanθ = 0. So, θ= pi, 2pi, 3pi, ...
At θ = pi, the SC stub produces a pass-band, and since θ=βl; β=ω/Vp, Vp= phase velocity:
θ=pi=(2pifp/Vp)lsc; fp= pass-band frequency, λg = guided wavelength, lsc = short circuited stub length. This gives lsc,
lsc = Vp/(2 fp) = λg/2
This gives lsc = 16.6mm for a pass-band frequency of 4.92 GHz.
Also, at 3-dB cutoff frequency (ωc), the susceptance of the equivalent circuit = susceptance of a low-pass filter prototype with one pole. Hence,
Ys cotθ + 1/(ωc Ls) = 1/100 ; ωc = 3-dB cut-off frequency.
So, we have three equations,
Ys cot (θ) - 1/(ω0 Ls) = 0 -> (1)
(Zs ωp Ls tanθ)/(ωp Ls + Zs tanθ) = 0 -> (2) or Ys cot (θ) - 1/(ω0 Ls) = ∞
Ys cotθ + 1/(ωc Ls) = 1/100. -> (3)
with lsc = 16.6mm at θ = pi.
Now, can anyone help me solve these equations to deduce the values of Zs, Ls.
Please help!