111/01/08 ENE 490 Applied Communication Systems Lecture 6 High-Pass, Bandpass, and Bandstop Filter Design

211/01/08 Review  RF filter design - Low-pass, high-pass, bandpass, and bandstop response - Low pass prototype circuit - Butterworth, Chebyshev, and Bessel filters - Design procedures

311/01/08 High-pass filter design (1) 1. Use all attenuation responses curves for the low-pass filters by simply inverting f/f c axis. 2. After finding the response which satisfies all of the requirements, refer to table of low-pass prototype values. Simply replace each filter element with an element of the opposite type and with a reciprocal value. For example, in the low pass prototype circuit shown in the next page, the value of L 1 of Fig. (B) is equal to 1/C 1 of Fig. (A),C 2 = 1/L 2,and L 3 = 1/C 3.

411/01/08 High-pass filter design (2)

511/01/08 High-pass filter design (3) 3. Scale the network in both impedance and frequency using these same equations for low-pass scaling: and

611/01/08 Ex1 Design and LC high-pass filter with and f c of 60 MHz and a minimum attenuation of 40 dB at 30 MHz. The source and load resistance are equal to 300 Ohms. Assume that a 0.5-dB passband ripple is tolerable.

711/01/08 The Dual network (1) The schematics located either above or below the tables of low-pass prototype produce exactly the same attenuation, phase, and group-delay characteristics, and each form is dual of the other.

811/01/08 The Dual network (2) Any filter network in a ladder arrangement can be changed into its dual form by application of the following rules: 1) Change all inductors to capacitors, and vice-versa, without changing element values. Thus, 3 henries become 3 farads. 2) Change all resistances into conductances, and vice- versa, with the value unchanged. Thus, 3 ohms becomes 3 mhos, or 1/3 ohms. 3) Change all shunt branches to series branches, and vice- versa. 4) Change all elements in series with each other into elements that are in parallel with each other. 5) Change all voltage sources into current sources, and vice-versa.

911/01/08 The Dual network (3) Dual networks are useful in the case of equal terminations when you desire to change the topology of the filter without changing the response to for example, eliminate an unnecessary inductor (causes higher losses)

1011/01/08 Bandpass Filter Design (1) The low-pass prototype circuits and response curves can also be used in the design of bandpass filters. Specifying the bandpass attenuation characteristics in terms of the low-pass response curves can be done by the following: 1. The attenuation bandwidth ratios remain the same, where, BW = the bandwidth of the required value of attenuation BW c = the 3-dB bandwidth of the bandpass filter

1111/01/08 Bandpass Filter Design (2) Often, the requirements are given as attenuation values at specified frequencies as shown by the curve in the next page. Therefore you must transform the stated requirements into information that takes the form of the equation above. The frequency response of bandpass filter exhibits geometry symmetry. That is it is only symmetric when plotted on a logarithmic scale. The center frequency is given by the formula: by using this formula, we are able to find the bandwidth at the specified attenuation and by referring to the bandpass response shown below, we can write

1211/01/08 Bandpass Filter Design (3)

1311/01/08 Bandpass Filter Design (4) 2. Refer to the low-pass attenuation curves provided in order to find a response that meets the requirements of step 1.  The actual transformation from the low-pass to the bandpass configuration is accomplished by resonating each low-pass element with an element of the opposite type and of the same value. All shunt elements of the low-pass prototype circuit become parallel-resonant circuits, and all series elements become series- resonant circuits as shown.

1411/01/08 The frequency- and impedance-scaling are done by using the following formulas. (1) For the parallel resonant branches, For the series-resonant branches,

1511/01/08 The frequency- and impedance-scaling are done by using the following formulas. (2) where, in all cases, R = the final load impedance B = the 3-dB bandwidth of the final design f o = the geometric center frequency of the final design, L n = the normalized inductor bandpass element values, C n = the normalized capacitor bandpass element values.

1611/01/08 Ex2 Design a bandpass filter with the following requirements: f o = 75 MHz, Passband ripple = 1 dB BW 3dB = 7 MHzR S = 50  BW 40dB = 35 MHzR L = 100 

1711/01/08 Bandstop filter design (1) The filter that a certain group of frequencies is rejected (opposite to bandpass filter) The design steps are pretty similar to that of the bandpass filter, 1. Define the bandstop requirements in terms of the low-pass attenuation curves. This is done by where the location of each frequency is illustrated as shown in the next page.

1811/01/08 Bandstop filter design (2) Read directly off the low-pass attenuation curves by substituting BW c /BW for f c /f on the normalized frequency axis.

1911/01/08 Bandstop filter design (3) 2. Each shunt element in the low-pass prototype circuit is replaced by a shunt series-resonant circuit, and each series-element is replaced by a series parallel-resonant circuit. This is shown below.

2011/01/08 Bandstop filter design (4) 3. The impedance and frequency scaling can be done using the following formulas.  For all series-resonant circuits:  For all parallel-resonant circuits:

2111/01/08 Bandstop filter design (5) where, in all cases, B = the 3-dB bandwidth R = the final load resistance f o = the geometric center frequency C n = the normalized capacitor band-reject element value, L n = the normalized inductor band-reject element value.