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 band-pass 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, Impedance-Matching Networks, and Coupling Structures", which sells for $114 on Amazon.

Got some filter data you'd like to share with us? This email address is being protected from spambots. You need JavaScript enabled to view it.

Below is a clickable outline for our filter discussion (some stuff is still missing!)

Absorptive versus reflective filters

Low-pass, high-pass and band-pass

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 flatnessSome seemingly simple filter examples

RF choke

DC return

DC block (moved to a new page)

Bias tee (moved to a new page)

EMI filterLumped 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 low-pass filter. Yes we will add some figures here soon!!!

**High-pass 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 high-pass filter.

**Band-pass filter (BPF)**

A band-pass 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 quarter-wave coupled lines.

Content has been moved here.

**Reentrant modes**

Sometimes when you design a band-pass 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 coupled-line filter, It uses quarter-wave 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 band-pass filters are followed by a low-order low-pass 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 is a lumped element RLC circuit, sometime called "tank circuit". Why the term "tank?" Because an LC resonator can store energy in the form of an AC sine wave, 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 nano-Henries and C is in pico-Farads. 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 zero ohms (an short 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 short 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 quarter-wave 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 high-value 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 low-pass 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 (equal-ripple 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 lumped-element filters. You should also check out the instruction page for our our free download for designing three, four and five-pole Chebyshev filters!

**Bessel-Thomson (maximally flat group delay)**

Best in-band group delay flatness, no overshoot, lowest stopband attenuation for given order and percentage bandwidth (ideal for receiver applications such as image-rejection filters).

**Butterworth (maximally flat amplitude)**

Best in-band 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 parallel-coupled, direct-coupled, 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.