microwave engineering
DESCRIPTION
Filter DEsignTRANSCRIPT
Microwave Filters
1
Filter and it’s requirements
• Filter is a two port network, used to control the frequency response of the system.
• For a band of frequencies, the gain is high, called “Pass band”.
• In other part of band, it attenuates, called “Stop band”
• Ideally, A filter requires :
– Zero Insertion loss in pass band
– Infinite insertion loss at stop band
2
Design methods
• So far, at microwave frequencies, three possible design procedures been
followed
• Periodic structures
• Image parameter method
– By providing cut off frequencies and available component values, a simple design of
filter is possible. But we can’t control the pass or stop band attenuation. Once we
designed for a frequency, it can’t be explored to another frequencies. Since the inaccurate
lumped elements been utilized, the quality of design limited
– Constant-k filter
– m-derived filter
• Insertion loss method
3
Insertion loss method
• While older methods are forward design (from specification to
observation), insertion loss method provides a reverse engineering method
• Following advantages
– Design for the required “Frequency response” with right specifications
– Flexible with design frequencies/characteristics impedance
– Trade off on design and implementation complexity
– Easier
• In this method, the power loss is fundamental specification:
• Power loss ratio PLR = Power available from source
Power delivered to load
can be expanded in polynomial
series in ω2
4
As:
or
• Based on the selection of M and N, there are four possible design type been
explored, so far.
• Namely:
– Maximally flat or Butterworth or Binomial Filter
– Equal Ripple or Chebyshev Filter
– Elliptical Filter
– Linear Phase Filter
5
Maximally flat or Butterworth or Binomial Filter
• The prototype low pass response is defined as (using Binomial series)
• N is order of the filter, ωC is cut off frequency (angular)
6
Equal Ripple or Chebyshev Filter
• The prototype low pass response is defined as (using chebyshev polynomial)
• TN(x) is chebyshev polynomial, N is order of the filter
7
Butterworth Vs Chebyshev
8
General Design Procedure
N, fc, MF or ER,
IL at pass band
and Stop band
To LP,
BP, HP,
BS filters
9
• Consider a two-element (2nd order) low-pass filter
• The input impedance:
• And the input reflection coefficient:
• And, Power loss ratio
Maximally Flat Low-pass filter – Prototype design
10
• From both equation,
• Now compare this equation with “Maximally flat response” with ωc=1 (normalizing
with cut-off frequency)
• By simple algebra, [available in Pozar- pp. 392-393]
11
• This same procedure has been extended to calculate for higher order filters and the
lumped elements (normalized to source impedance) are tabulated.
• Two possible approached
1. First element is capacitor
2. First element is Inductor
12
C
IL
N
10
2010
log2
110log
13
Equal Ripple LPF - prototype
• For Equal Ripple following specifications are important
– Stop band IL (dB) - IL
– Ripple Magnitude (dB) - R
– Cut-off frequency- fc
• From these, the order of the filter can be calculated:
C
R
IL
N
1
10
101
cosh
110
110cosh
14
15
Example
• Solution:
– Actually we have to calculate the order of the filter
• IL=20dB at 11GHz, fC=8GHz
C
IL
N
10
1010
log2
110log
4
44.3
811log2
110log
10
10
20
10
N
N
16
C
R
IL
N
1
20
201
cosh
110
110cosh
Assume R = 0.5 dB
N = 5.5 … that’s “6”
For chebyshev response: