Microwave
filters
Updated
April 18, 2014
Click
here to go to a page that explains filter schematic symbols
(link fixed thanks to Rhian!)
Click
here to go our page on lumped element filters
Click
here to go to a page on filter group delay
Click
here to go to a page on diplexers
Click here
to go to our page on YIG components
A note from the Unknown Editor:
many textbooks have been devoted to filter design. We don't intend
to assimilate all of this knowledge here, our goal is, as always,
to provide you with a basic understanding of the subject and hook
you up with some vendors that can help you out. For the near future
we will concentrate mostly on planar bandpass filters, then follow
up with some lumped element examples.
New for August 2012: Go to our download area and grab a free copy of Mattaei, Young and Jones "Microwave Filters, ImpedanceMatching Networks, and Coupling Structures", which sells for $114 on Amazon.
Got some filter data you'd like
to share with us? Shoot
it in!
Below is a clickable outline
for our filter discussion (some stuff is still missing!)
Common
filter terminology
Absorptive
versus reflective filters
Lowpass, highpass and bandpass
Multiplexers (separate
page)
Diplexers (separate page)
Reentrant modes
Resonances of RLC circuits
Parallel LC resonance
Series LC resonance
Quality factor
Bandwidth
Order of a filter
Poles and zeros
Stopband attenuation
Overshoot
Group delay flatness
Some seemingly
simple filter examples
RF choke
DC return
DC block (moved to
a new page)
Bias tee (moved to
a new page)
EMI filter
Filter
response types
Chebyshev
BesselThomson
Butterworth
Gaussian
Lumped
element filters (separate page)
Group
delay of filters (separate page)
Planar resonator filters for
microstrip or stripline (coming soon on a separate page)
Will include: topologies,
design considerations, tolerance effects, cover effects for
microstrip filters, design equations, detailed design procedure,
and references.
Waveguide filters  how about
someone out there contribute on this topic for us?
Commonly
used terminology for microwave filters
Filters are typically two port
networks. They rely on impedance mismatching to reject RF energy.
Where does all the energy go? That's up to you as a designer to
figure out, and a big reason why filters are typically located between
attenuators or isolators. Our page on transmission
line loss will explain the difference between attenuation and
rejection.
Absorptive
versus reflective filters
Filters that are matched outside of their stop band are called "absorptive
filters". One way to make a reflective filter into an absorptive
filter is to add an isolator
to the filter's input. Another way to do this is to use a diplexer
and terminate the unwanted band.
Lowpass
filter (LPF)
This is a filter that passes lower frequencies down to DC, and rejects
higher frequencies. A series inductor or shunt capacitor or combination
of the two is a simple lowpass filter. Yes we will add some figures
here soon!!!
Highpass
filter (HPF)
The opposite of a low pass filter, an HPF passes higher frequencies
and rejects lower ones. A series capacitor or shunt inductor or
combination of the two is a simple highpass filter.
Bandpass
filter (BPF)
A bandpass filter has filter skirts both above and below the band.
It can be formed by cascading a LPF and HPF, or using resonant structures
such as a quarterwave coupled lines.
Multiplexer
Content has been mnoved here.
Reentrant
modes
Sometimes when you design a bandpass filter for 10 GHz, it also
passes RF at 20 GHz or 30 GHz or 40 GHz. These are called reentrant
modes.
Below is an example of an coupledline
filter, It uses quarterwave sections as couplers, they couple similarly
at their 3/4 wave, 5/4 wave, etc. frequencies. These are the third,
fifth etc. harmonic frequencies.
In the figure you can see the passband at 10 GHz, and the reentrant
mode at 30 GHz (3/4 wave frequency).
Reentrant mode example

Often bandpass filters are followed
by a loworder lowpass filter to dispose of the reentrant modes.
Resonance
of RLC circuits
Resonance is a term used to describe the property whereby a network
presents a maximum or minimum impedance at a particular frequency,
for example, an open circuit or a short circuit. Resonance is an
important concept in microwaves, especially in filter theory. One
simple form of resonator are lumped element RLC circuits, sometime
called "tank circuits". Why the term "tank?"
Because an LC resonator can store energy in the form of an AC sinewave,
much like a pendulum "stores" gravitational energy.
The resonance of a RLC circuit
occurs when the inductive and capacitive reactances are equal in
magnitude but cancel each other because they are 180 degrees apart
in phase. When the circuit is at its resonant frequency, the combined
imaginary component of the its admittance is zero, and only the
resistive component is observed. The sharpness of the minimum depends
on the value of R and is characterized by the "Q" of the
circuit.
The formula for resonant frequency
(in Excelese) of an LC circuit is:
F=1/(2*PI()*SQRT(L*C/1000))
where F is in GHz, L is in nanoHenries
and C is in picoFarads. Click here
to go to our resonant frequency calculator!
Parallel
LC resonance
Resonance for a parallel RLC circuit is the frequency at which the
impedance is maximum. Plotted below is the special case where the
resistance of the circuit is infinity ohms (an open circuit). With
values of 1 nH and 1 pF, the resonant frequency is around 5.03 GHz.
Here the circuit behave like a perfect open circuit. Note
that for R=Z0, at the resonant frequency the response would hit
the center of the Smith chart (the arc would still start at the
short circuit but would be half the diameter shown). At zero GHz
(DC) as well as infinite frequency, the ideal parallel LC presents
a short circuit.
Parallel Resonance,
C=1pF, L=1nH, R=open circuit

Series
LC resonance
Resonance for a series RLC circuit is the frequency at which the
impedance is minimum. Plotted below is the special case where the
resistance of the circuit is infinity ohms (an open circuit). With
values of 1 NH and 1 pF, the resonant frequency is around 5.03 GHz.
Here the circuit behave like a perfect short circuit. Note
that for R=Z0, at the resonant frequency the response would hit
the center of the Smith chart. At zero GHz (DC) as well as infinite
frequency, the ideal parallel LC presents a open circuit.
Parallel Resonance,
C=1pF, L=1nH, R=short circuit

Some
simple filter examples
Sure, these look like very simple
designs. But nothing is ever as easy as it seems in microwaves!
RF choke
An RF choke is what engineers call something that doesn't pass an
RF signal, but allows a DC or low frequency signal to pass through.
Series inductors are often used as RF chokes, as well as quarterwave
structures like the one shown below. Here a capacitor forms an RF
short circuit, which is transformed to an open circuit at the input.
Such a capacitor is called a "bypass capacitor".
A highvalue resistor can also
be used to form an effective choke. If the resistance is high compared
to your transmission line's characteristic impedance, it chokes
off the RF.
DC
return
This is used to add a DC ground to an RF line. For example, in a
PIN diode switch, you need a path for a series diode's current to
return to.
DC block
A DC block is nothing more than a capacitor that has low series
reactance at the RF frequency, and allows you to separate DC voltages
along a transmission line. A parallel coupled line can also serve
as a DC block.
DC blocks can be placed in the
"hot" conductor of a transmission line such as coax, or
the ground plane, or both, as shown below. Many vendors offer coaxial
DC blocks in all three arrangements. When would you want a DC block
in the ground plane? Perhaps you want to inject a voltage onto the
source of a shunt FET, which is grounded to your fixture. Users
of this type of DC block must be aware that their equipment could
provide a voltage when they touch it. Careful where you drop that
wrench!
Three types
of DC blocks

EMI filter
EMI stands for "electromagnetic
interference", but you'd already know that if you studied our
Acronym Dictionary. EMI filters
are used to keep stray signals from polluting your design. Commonly
known as "feedthroughs", the basic EMI filter is a lowpass
filter, and uses a combination of shunt capacitance and series inductance
to prevent EM signals from entering your housing our enclosure.
Filter
response types
Chebyshev
(equalripple amplitude)
The Chebyshev filter is arguably the most popular filter response
type. It provides the greatest stopband attenuation but also the
greatest overshoot. It has the worst for group delay flatness (OK
for CW applications such as a frequency source). Check out our page
on lumpedelement filters. You should
also check out the instruction page
for our our free download for designing three, four and fivepole
Chebyshev filters!
BesselThomson
(maximally flat group delay)
Best inband group delay flatness, no overshoot, lowest stopband
attenuation for given order and percentage bandwidth (ideal for
receiver applications such as imagerejection filters).
Butterworth
(maximally flat amplitude)
Best inband amplitude flatness, lower stopband attenuation than
Chebyshev, better than Chebyshev for group delay flatness and overshoot
(usually used as a compromise). All of the above are realizable
in parallelcoupled, directcoupled, and interdigital filter topologies.
Gaussian
This filter provides a Gaussian response in both frequency and time
domain. It is useful in IF receiver matched filters for radar.
