RF: Broadband Matching

Introduction
Today at work, I came to the conclusion that Broadband matching is a fine art.  It takes years of experience to understand and get it right.  Even the most experienced RF Engineers still have issues developing a matching network for amplifiers and power transistors.

I'm going to give a brief overview of Broadband matching and how it applies to the RF engineer.

The Basics
A matching network is simply any network that can transform impedances from it's input to output.  Generally, they consist of either LC networks or microstrip equivalents.  They come in the form of filter type matches.  I have mostly used strings of networks with the high pass and low pass structure.

There are many ways to match networks and many structures you can use.  At low frequencies (under 1 GHz) and at narrow bandwidths (under 100 MHz) it's generally easier to match using the Smith Chart.  At higher frequencies and higher bandwidths, I recommend a more trial and error approach.  This is what broadband matching entails (higher bandwidths).  There is no single method to broadband matching, so I'll show you my method and then only with amplifier/transistors.

My Method
So let's say we have an RF amplifier that is denoted like so:

Every amp has an inherent input impedance and output impedance.  This is modeled by something like so:

Now generally, input impedances are meant to be extremely high (Megaohms in Op-Amps) but in RF amps they can be very small (sometimes 2 - 3 ohms).  The output can be almost anything, but generally smaller.

Now something to notice, is the inherent resistances.  Most of the time they are not strictly resistive and will be reactive as well.  I noticed today that the amp I was using was in fact inductive at high frequencies.  So I had to match accordingly.  

Since Rin = Lin, I began my matching with a series capacitor like so:

So you see, I used the internal inductor as my first component, then use the series capacitor to complete this first part of the match (High Pass Filter).

To shorten this post up a little bit, I will say that you will then put a shunt capacitor as the next component, then a series inductor, etc, etc.  Repeat those until you have a match.  Do the same for the output.

Now the big question you'll be asking is "what about the values?"  Well this is where the art comes in.  It's not a very simple topic to go through.  This is completely dependent on what frequency return loss goals you have and how many networks you have. I generally use an optimizer in Agilent's ADS Simulation Software (EESof).

But I will give you a general overview of what "type" of values you'll need for certain frequency ranges:

HIGH FREQUENCY (500MHz-2GHz)

• Shunt C: Very low values (0.1pF - 2pF)
• Shunt L: Medium values (50nH - 100nH)
• Series C: Medium RF values (20pF - 50pF) [These are more dependent on other factors]
• Series L: Very low values (1.6nH - 15nH)

LOW FREQUENCY ( < 500MHz)

• Shunt C: Medium values (100pF - 1uF)
• Shunt L: High Values (1uH - 100uH) [This is a guesstimate]
• Series C: High RF values (1000pF - 10uF)
• Series L: Medium values (100nH - 10uH)

I hope this post is somewhat useful.  I know it's vague on details but I want to give you an idea on broadband matching.  I can't really write a whitepaper on it for a post.  If you have specific questions email/comment and ask.  Later

--------------------

Justin Coulston

justin.coulston@gmail.com

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.

----------------------------
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.