RF and Microwave Frequency Circuits and systems RN620

Maximally Flat Microwave Filter Design

To design a maximally flat filter with 12dB attenuation at 1.3333 times cutoff frequency of 3.8GHz.

We have fc = 3.8 GHz

And at 1.3333 times fc

Attenuation = 12dBi.e. 10 log PLR = 12So, PLR = 15.84

Using PLR = 1 + k 2(w / wc ) 2N

N = 4.689 ≈ 5

Using g0 = gN+1 = 1And gn = 2 sin [(2n - 1) Π / 2N]; n = 1, 2... N

g1 = 0.618g2 = 1.618g3 = 2g4 = 1.618g5 = 0.618

And making impedance and frequency scaling with R0 = 50 Ω and ω c = 2 Π fc

Using L = L n ( R0 / ω c ) ;L n is normalized inductanceAnd C = C n / ( R0 ω c ) ;C n is normalized capacitance

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RF and Microwave Frequency Circuits and systems RN620

We get

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RF and Microwave Frequency Circuits and systems RN620

distributed component form

For a capacitance The impedance Z0 = 20 Ω

And effective electrical length (θ) = C ( Z0 / R0 )

For inductanceThe impedance Z0 = 100 Ω

And effective electrical length (θ) = L ( R0 / Z0 )

section θ

1 14.162 46.353 45.834 46.355 14.16

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RF and Microwave Frequency Circuits and systems RN620

Magnitude of lumped and distibuted

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RF and Microwave Frequency Circuits and systems RN620

Also the presence of the capacitance due to junction transition effect was simulated in ADS by using the microstrip step (MSTEP) component. The effect was not included in our calculation but is present in the actual board so we must take it into account if our design is to meet the given specifications.

From the figure we can see the effect of using the distributed component instead of the lumped components. Use of distributed component tends to deviate the curve from the lumped component curve at high frequencies. But we still have to make account if the transitional capacitance between microstrip lines. In that case we see there is a change in the attenuation again.Now to get as close as possible to the lumped curve, we change the length parameter of all the microstrips proportionally. We had to change the length of each microstrip to about 82% of the actual length required. Final curve after matching is given below.

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RF and Microwave Frequency Circuits and systems RN620

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RF and Microwave Frequency Circuits and systems RN620

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