LPF_6th_mf_si

Simulation of a 2.5 GHz low-pass filter with a maximally flat response using Qucs

a Tutorial by

Mahmoud Sadat

Hesham Sadat

Arab Academy for Science & Technology & Maritime Transport

Collage of Engineering and Technology

In this brief tutorial, we use Qucs to simulate a 2.5 GHz low-pass filter with a maximally flat response. The low-pass filter is fabricated on substrate with the dielectric constant of 4.6. In this tutorial we are not concerned about the design of this low-pass filter and we will focus our attention on using Qucs to simulate the structure and obtain its parameters. We will explain Qucs through that design example.

Design Example:

Design a 6th order low-pass filter with a maximally flat response and a cutoff frequency of 2.5 GHz. The filter impedance is RO = 50 Ω. Implement the filter using only microstrip with the highest and lowest practical impedance values of 120 Ω and 20 Ω.

Solution:

First, we need to get filter element values.

Table1: Element values for maximally flat low-pass filter prototypes

Thus, g1 = 0.517 = C1 g2 = 1.414 = L2 g3 = 1.932 = C3 g4 = 1.932 = L4 g5 = 1.414 = C5 g6 = 0.517 = L6

We want to implement this on a microstrip substrate with a thickness h = 1.58 mm, and a dielectric constant Єr= 4.6. For inductors, we make: βl = L× RO/ZH For capacitor, we make: βl = C×ZL/RO

Emtalk.com Microstrip line calculator

Qucs Microstrip line calculator

Section

Zi=ZL or Zh βl i

Wi (mm)

li (mm)

Wi (mm)

li (mm)

1 20 Ω 11.8º 10.68 2 10.67 1.98

2 120 Ω 33.8º 0.38 6.45 0.30 6.73

3 20 Ω 44.3º 10.68 7.5 10.67 7.42

4 120 Ω 46.1º 0.38 8.8 0.30 9.17

5 20 Ω 32.4º 10.68 5.48 10.67 5.43

6 120 Ω 12.3º 0.38 2.35 0.30 2.45

Figure3: Micro-strip layout of final filter

Figure2: stepped impedance implementation

Table2: Micro-strip line calculation

Figure1: Low pass filter prototype circuit

*Design steps in Qucs:

1) Run Qucs Program. You will see a layout similar to that shown in Figure1.

2) Click the new button as shown in Figure 4

Figure4

3) Click the button as shown in figure 5, and choose transmission lines.

Figure5

4) Drag the microstrip line to the blank page from transmission lines library as shown in figure 6.

Figure6

5) In our design we need 6 microstrip lines so we copy it or insert it 6 times as shown in figure 7.

Figure7

6) Select wire as shown in figure 7 to connect the microstrip lines, Click the bottom as shown in figure 8 and choose sources, and select power source then place one in input port and another one in output port.

Figure8

7) Connect power sources to the circuit using wire then insert ground to each source as shown in figure9.

Figure9

8) Choose substrate from transmission lines as shown in figure 10 .

Figure10

9) Choose S parameter simulation from simulation library as shown in figure 11.

Figure11

10) Click on insert then choose insert Equation and drop it to the page as shown in figure 12.

Figure12

11) Now we want to implement our design example so, we need to get the values of width and length using microstrip line calculator provided by qucs .By click on tools then choose line calculation we get microstrip calculator as shown in figure 13. (Note: change all parameters with mil unit to mm).

Figure13

12) We use values of βℓ,Zi in Table2 to calculate W,L using microstrip calculator in addition to the values of freq. , H and Єr provided in the design example then press synthesize to get values of W,L Change values of W,L in each Microstrip line section in the circuit with its corresponding value calculated in table2 ,and change the sub-strate subst1 er from 9.8 to 4.6 and h from 1 to 1.58 as shown figure 14.

Figure14

13) Now we want to make our simulation sweep the freq. from 1Ghz to 5Ghz to see the filter response so we change at the s-parameter the start and stop to 1GHz and 5GHz respectively and make the number of points 91 , to see the response in dB we have to make the output to be calculated in dB by adding equation calculate S21 in dB using command dB(s[2,1]) will calculate it in dB. ex: s21_db=dB(s[2,1]) as shown in figure 15.

Figure15

14) Click on simulate to start simulation then will need to choose the diagram from diagrams library for our example we will select Cartesian then double click on S21_dB then click ok to plot it against frequency as shown in figure 16 . (Note: you can edit the graph properties from properties tap for example adding grid etc)

Figure16

15) After finishing the selection of parameter s21_db it will be plotted against frequency as shown in figure 17. (Note: you can add marker to the graph by press on icon in figure 14)

Figure17