RF: High Frequency Filter Design Considerations

There are times as an Electrical Engineer when you just wish to be given the answer to all your High Frequency Design issues.  Unfortunately, I'm not here to do that.  Instead, I'm going to give you a basic way to view all High Frequency Application design.  I'll use the design of a filter as an example.

Filter Design Basics
To start, you need a basic understanding of filter design.  There are 4 main filter types (5 if you include All-Pass Filters): Low-pass, High-pass, Bandpass, Band-reject/Bandstop.  These 4 types are the building blocks of all filtering schema.  The two we will focus on primarily are Low-pass and High-pass filters.

Figure 1: Low-pass Lumped Element Example

Figure 2: High-pass Lumped Element Example

An Electronic Filter by definition is an object or process that removes undesired components or features.  In our usage, an Electronic Filter is a hardware arraignment that allows and rejects certain frequency ranges.  There are many ways to create filters.  Filters can be constructed with lumped elements, waveguides, microstrips, and more.  Each of these construction types has certain characteristics that make them better to design with than others.  The main characteristic most engineers are concerned with are bandwidth capabilities and the amount of space the filter will take up.

Since we are talking about "High Frequency" filters we would do best to talk about microstrip design.  Unfortunately, this topic is very extensive and too detailed to put in one post (if you would like more information on this feel free to email me).  So I will stick with the basic lumped element structure that all filters are based.

Lumped Elements (Capacitors, Inductors, Resistors)
Realistically, lumped elements can be used to design filters up to 4 GHz. Most people, though, cannot accomplish this easily.  Even the most skilled engineers can only design filters up to 2 GHz.

So why is this so difficult?

The difficultly lies in the in the fact that no components are perfect.  Inductors, Capacitors, and Resistors all have something called parasitics that naturally occur due to the physical construction of the parts.  Below are the (more) accurate models for a capacitor and inductor.

Figure 3: Capacitor Model

Figure 4: Inductor model

As you can see, each model has elements of the other fundamental components.  If you look at an inductor, you'll notice that the windings are turned very close together.  This close proximity creates a capacitance in parallel with the ideal inductor.  Also, since there are no super-conductors in use in practical electronics, we have a resistance due to the wire (AKA Equivalent Series Resistance).  The same is true for the capacitor.  There is a parasitic resistance and inductance due to the leads of the capacitor.  All this information can be obtained from a parts datasheet.

Some Component Manufacturers:

• Kemet Electronics - Capacitors
• ATC(American Technical Ceramics) - Capacitors
• CoilCraft - Inductors
• Ohmite - Resistors

Manufacturers are constantly trying to eliminate these parasitics because they are "unwanted" characteristics of parts.  These "unwanted" characteristics become vital at frequencies above 900MHz.  These problems occur when the reactances of the parasitics become very close to each other.  As frequency increases, say for instance within an inductor, the inductor's L will rise higher and higher while the capacitance will go lower and lower based on the below equations:

Equation 1: Capacitor Reactance Equation

Equation 2: Inductor Reactance Equation

When these two reactances are equivalent, we call this the resonant frequency.  This frequency is where the the function of the component switches.  After this point a capacitor then acts like an inductor and an inductor acts like a capacitor.  The resonant point of a component is vital in deciding what manufacturer to purchase from.  If you are trying to obtain adequate results, lets say at 2GHz, but your component's resonant frequency is close to 600MHz, this component will not do the you any good (unless of course you'd prefer it to be used as an inductor).

Example High Frequency Filter
Below I have the circuit and gain response of a simple High-pass filter (cutoff at 1.6GHz) excluding the natural parasitics.  You can see, the response is relatively flat and there are no known issues (minus the fact that it doesn't get very close to 0dB).

Figure 5: 5th-Order Chebyshev High-pass Filter

Figure 6: Gain Response of High-pass circuit (no parasitics)

Now look at the new circuit with included parasitics (Note: I used common parasitic values. They are close to parts I regularly use).

Figure 7: 5th-Order Chebyshev High-pass Filter (w/ Parasitics)

Figure 8: Gain of High-pass Filter (w/ Parasitics)

The differences may be subtle but can be drastic the higher in frequency you go.  Since this filter is running at the 1.6GHz level, there aren't a lot of issues.  Still there are a number of parasitics not taken into account.  If you were to take realistic data, you would notice large downward spikes in the passband.  These are due to grounding issues on the board and parasitics within the PCB board itself.  These can become relatively important especially past 2GHz.  A note to add on this blog, is that I used B2Spice to do the calculations.  Unfortunately, I'm not as familiar with this software as I am with ADS (Agilent's Advanced Design System) which in my opinion is a much stronger piece of software.  Unfortunately, I don't have private access to this software and must settle with B2SPICE for the time being.

I hope this tutorial was helpful, in the very least, in teaching you how high frequency components must take into account the effects of parasitics.  You should include parasitics in all simulations (whether filters or not) above 500MHz (and some below depending on components).  They become a driving point in design.

I have below a few books available on Amazon.com that can be useful in filter design.  I have used these personally and know that they can explain this topic in a much better way than I.  If you have questions or topics you wish to here about, respond to this post or email me at: Justin.Coulston@gmail.com.

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JColinator
RF Hardware Electrical Engineer
B.S. Electrical Engineering

Notes: This book is a little dry but very informative if you can follow along.  It's a complete proof on Filter and Filter Synthesis












Notes: I use this book at work on a regular basis.  It has all the basics of RF circuit design.  It contains more detailed information on microstrip filter design and lumped element design.  It also goes over all the basic of circuit parameters (ABCD-parameters, S-parameters, etc)









Notes: Another favorite book of mine that goes into the same kind of depth the RF Circuit Design book does.  This one, though, has more information specific to wireless design including Antenna Design and practical techniques.