Passive LC Filter
Design and Analysis

Using measurement-based models for design and analysis
Passive electronic LC filters are used to block noise fromcircuits and systems. Ideal filters pass the required signal
frequencies with no insertion loss or distortion, and completely block all signals in the stop-band. Real filters have
DC and AC resistances that contribute to insertion loss,
requiring careful component selection.
Selecting the exact values of the components required
for a particular application may appear to be a daunting
task for beginners. Filter categories include lowpass,
highpass, bandpass, bandstop, all-pass, and multiplexers.
The simplest to design and implement are the lowpass
and highpass types.
A number of possible filter alignments exist, including
Butterworth, Bessel, Chebyshev, and elliptic. Selectionof the filter alignment involves trade-offs in flatness of thefrequency behavior versus sharpness of the cut-off. Thevery simplest LC filter consists of an inductor and a capacitor. Higher-order filters use more components to givea sharper, more defined roll-off for better attenuation ofunwanted noise. See Appendix A for details.
The good news is that modern circuit synthesis and analysis
programs can quickly perform the otherwise tedious andtime-consuming calculations. Filter synthesis programs
generate the required inductance (L) and capacitance (C)values. Analysis programs simulate the results after the user
enters the appropriate values. Once the initial ideal values
have been calculated, practical solutions are created using
off-the-shelf components.

Modeling Filter Behavior
Ideally, one could simply define the band of frequencies
to be passed, those to be blocked, and a program wouldgenerate standard component values resulting in theactual on-board performance.
Free programs for generating basic filter designs are available on the internet, such as Design LC Filters (V 3.0) at
http://www.wa4dsy.net/filter/filterdesign.html. Programs likethis synthesize a filter design using ideal element values asa starting point. If the design results are not standard values,
some compromises in performance may be necessary.
Substitute standard part values and run a circuit simulation
to determine effects on the filter performance.

Coilcraft offers a wide variety of tight-tolerance ceramic chip
inductors, SPICE models, and design support.

For lower-frequency filter designs, ideal component models may be sufficient for analysis. However, the effects ofcircuit parasitics of inductors, capacitors, and circuit board
traces may require selection of slightly different component
values to tune the performance of higher-frequency filters.
In this case, for better prediction of the real filter, accurate
inductor models and circuit board trace and pad models
should be involved. For many designs, accurate inductancemodels based on actual component measurements arenecessary, but ideal capacitors can be used for the simulation. Simulations of filters approaching the Gigahertz range
may require non-ideal capacitor models as well.
Coilcraft offers free, accurate, measurement-based models of many off-the-shelf inductors, including detailed
instructions for implementing them in popular simulation
programs, at this link: http://www.coilcraft.com/models.cfm.
These inductor models help get your filter design closer
to real performance than simpler, ideal inductor models.
Finally, a prototype board should be assembled, tested,
and tweaked if necessary. Once the design appears to beacceptable, analysis of the effects of component tolerances
can be performed.

Demonstrated Low Pass and High PassSolutions
To simplify LC filter design, Coilcraft has created LC filter
reference designs, including 3rd order Butterworth lowpass and high-pass, and 7th order elliptic filters. Thesedesigns demonstrate the high performance that can beachieved using Coilcraft inductors and standard capacitors.
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References
Rhea, Randall W., HF Filter Design and Computer Simulation (Noble Publishing Corporation, 1994)
Vizmuller, Peter, RF Design Guide (Artech House, Inc.,1995)
Williams, Arthur B., Electronic Filter Design Handbook(McGraw-Hill, 1995)

Appendix A – Filter Alignments and Properties
Butterworth – Maximally flat (more linear) pass-band
response, slower roll-off, flat stop-band response. Requires
a higher order to achieve a specific stop-band spec. vs.
Chebyshev and Elliptic.

Chebyshev (Type 1) – More pass-band ripple, sharperroll-off, flat stop-band response
Chebyshev (Type 2) – Flat pass-band response (requires
more components), sharper roll-off, more stop-band ripple
Elliptic (Cauer) – Sharpest roll-off, more pass-band
ripple and stop-band ripple. Equiripple elliptic filters are
maximally insensitive to component variation.
Bessel – Maximally flat group delay (maximally linear
phase response) that preserves the wave shape of signals
in the pass-band.
Increasing the number of filter elements increases theperformance of the filter.
The following curves are the results of 5th order, low pass filters.

Butterworth

Chebyshev type 1

1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.20.2

000

0.2

0.4

0.6

0.8

1.0

00.2

Chebyshev type 2

0.4

0.6

0.8

1.0

0.8

1.0

Elliptic

1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

000

0.2

0.4

0.6

0.8

1.0

0

0.2

0.4

0.6

Source: http://en.wikipedia.org/wiki/Electronic_filter

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