RF Circuit Designer's Notes

Little nuggets of RF/analog circuit theory and design. Learn with me about PLLs, Q, noise, oscillators, filters, digital receiver concepts, etc.

Wednesday, October 20, 2004

Circular waveguides and the can-antenna for 802.11

Circular waveguides used as antenna.

TE11 mode
D = 0.586*lambda_o

TMo1 mode
D = 0.766*lambda_o

TE21 mode
D=0.97*lambda_o

Below cutoff, the signal is attenuated.

Best to operate in TE11 mode. If other modes are excited, the antenna pattern will became skewed and the maximum will not be on the boresite. TM01 modes seem ok though. But for TE21 modes and higher, the pattern is skewed. The pattern information came from an online microwave antenna book.

The length of the can matters somewhat too. Ideally the aperture should be at a standing wave maximum point. So the length ought to be 3/4 LG (guide wavelength, not free space wavelength)


Tuesday, October 19, 2004

PLL Synthesizer Design

The main goal of PLL synthesizer designs is to optimize the VCO's phase noise with a lower phase noise reference, usually crystal-based. There is a tradeoff between tuning range and phase noise.


By overlaying the plots of the VCO phase noise and multiplied-up reference phase noise, one can see a frequency where the plots intersect. The composite phase noise plot is usually the multiplied-up reference phase noise near the carrier and the VCO itself far away from the carrier. With pictures it's easier to describe.

The intersection of the plots occurs at FC. This frequency will be the PLL's loop BW.

General method
1. Start with simple first order PLL loop (only one integrator-the VCO)
2. Determine loop gains needed to obtain FC.
T=KP*G*KV/(N*2pi*f)
KP units: V/radians (or A/radians for charge pump output)
KV units: Radians/(sec*V)
G: unitless or a transresistance for charge pump output
T=1 at f=FC

3. Now make loop 2nd order or higher. Add integrator (with pole at DC and zero)
Choose zero location based on acceptable phase margin at FC

4. Add other poles at f>FC due to VCO tuning bw, opamp pole, etc..
Calculated phase margin at FC

Quick estimate of phase lag or lead due to poles and zeros
Zeros
for fz < FC
+90-180/pi*(fz/FC)
for fz > FC
+180/pi*(FC/fz)

poles
for fp < FC
-90+180/pi*(fp/FC)

for fz > FC
-180/pi*(FC/fz)



Thursday, October 14, 2004

book review

I like amazon's book reviews of technical books. Most trade mags hype up the book and never say anything nasty.


Circuit Design for Audio, AM/FM, and TV.
Author: Texas Instruments
pub in 1967!!!!

I found this book in the library. I loved it. This presents lots of circuits with design procedures to make a real circuit with real circuit values. It's not a dumbed-down superficial cookbook. It has enough equations, design insights and data to make a circuit.
I'm going to order this book or its earlier incarnations as a series of four paperbacks.



Tuesday, October 12, 2004

Q -1

Basic calculation of Q for resonant LC tanks

Parallel RLC
Q= Rp/|Zp(wo)|

Series
Q=|Zs(wo)|/Rs

More facts:
|Zp(wo)|=|Zs(wo)|=SQRT(L/C)
This ratio is also known as the characteristic impedance of the tank.

This makes sense because we want Rp high or Rs low to minimize the loss.


Extra Element Theorem

I was looking through my files and re-read an old article about the Extra Element Theorem.
This theorem is cool because enables you to analyze a network by removing or adding an element that makes the analysis easier. For example, the input impedance of a bridge circuit with a load on the detection nodes. Without this theorem, I would have done the analysis using nodal or mesh analysis and coming up with a bunch of linear equations. Then I would have to remember Kramer's rule to solve for the variable. The end result is a mess of algebra that gives little insight into the circuit behavior vs. parameters.
The EET allows one to remove the load, analyze three modified bridge circuits (Rin, R looking into the nodes where the element was removed, with the input opened and shorted) and express the result in terms of parallel and series combinations of resistances.

The EET is simple to remember for finding the input Z of any network.
But for finding the transfer functions, it's harder. I couldn't figure it out in 10 minutes.



Saturday, October 09, 2004

Broadband coupler

I finally got the article that explains broadband coupler design. The coupler is based on the resistive bridge. The coupled port forms one of the arms of the bridge and it is also ground referenced. The DUT port forms another arm of the bridge. Unfortunately, that arm is not ground referenced. To measure a DUT that is ground referenced, a balun is needed to convert the DUT to floating load for the bridge.

This article helped me alot to understand what's going on in the VNA bridge. It doesn't mention the tricks needed to get the bridge working up to several GHz, such as the balancing the parasitic capacitances of the bridge components.

The article is "Simple SMT Bridge Circuit Mimics Ultra-Broadband Coupler" by Joel Dunsmore in RF Design magazine, Nov. 1991, pgs 105-108.

I'll scan the article and put a link to it later.

Thursday, October 07, 2004

High Frequency Behavior of Ferrites

I previously thought that the ferrite beads became lossy at high frequencies and that loss stays constant as f goes up. RB said a ferrite bead model is a parallel RLC circuit. At low frequencies, it is mostly inductive with resistive loss, then the inductive component decreases and the losses dominant. At sufficiently high frequency the parasitic capacitance between the ends of the bead begin to take effect and short out the lossy path.

Now I understand why the ferrite-loaded transmission line balun uses a string of beads with different permeabilities (mu). The high mu stuff works great at low frequency, but its lossy path begins to short out also at lower frequency. Hence, the balun needs low mu stuff which is still an effective loss element at higher frequencies.

hot end ======================== cold end
AAAABBBBCCCCDDDDDD
low mu high mu