1. EEE 194RF_ L12Low and High-Pass Filter Examples1 ELEC 412 RF & Microwave Engineering Fall 2004 Lecture 12 Low and High Pass Filter Examples

2. EEE 194RF_ L12Low and High-Pass Filter Examples2 Low-Pass Filter Design Example Design a Low-Pass Filter with cut-off frequency of 900 MHz and a stop band attenuation of 18 dB @1.8 GHz. From the Butterworth Nomograph, A max = 1 and A min = 18. A max = 1 since unity gain. And the order of the filter is N = 3. From Butterworth Tables, g 1 = g 3 =1.0 and g 2 = 2.

3. EEE 194RF_ L12Low and High-Pass Filter Examples3 Transformation From Low-Pass Filter

4. EEE 194RF_ L12Low and High-Pass Filter Examples4 Normalized Lumped Parameter values What to do with the g k ‘s and Where f c is the cutoff frequency and L k_norm and C k_norm are normalized element values

5. EEE 194RF_ L12Low and High-Pass Filter Examples5 P5.7 Low-Pass Filter Design The normalized lumped element values: g0=1; g1=0.7654/(2  f c ); g2=1.8478/(2  f c ); g3=1.8478/(2  f c ); g4=0.7654/(2  f c ); g5=1.;

6. EEE 194RF_ L12Low and High-Pass Filter Examples6 Denormalized Lumped Parameter Values and For all filter configurations

7. EEE 194RF_ L12Low and High-Pass Filter Examples7 Low-Pass Filter Design Example

8. EEE 194RF_ L12Low and High-Pass Filter Examples8 Low- To High-Pass Transformation Transform the Low-Pass Filter Normalized Component Values to the Normalized High-Pass Values Inductors in Low-Pass Configuration Become Capacitors in High-Pass. Capacitors in Low-Pass Configuration Become Inductors in High-Pass

9. EEE 194RF_ L12Low and High-Pass Filter Examples9 Denormalized Lumped Parameter Values and Same as that for the Low-Pass Filter

10. EEE 194RF_ L12Low and High-Pass Filter Examples10 De-Normalizing Filter Component Values All Normalized Component Values Are De- Normalized Using the Following: and