4×10 Workbench with Pneumatic Lift

I wanted a large workbench with surface dimensions a bit larger than the standard 4×8 foot material I frequently work on. I also wanted it (almost) rock-solid to do some optics-related work. The workbench is very heavy- but I designed in pneumatic lifters so that I can easily put the bench on wheels when I want to move it around. Link to Paper.

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Potato Cannon with Chronograph- Part I

Details about building a pneumatic-based potato cannon. The more interesting part is its performance assessment. Link to Part I.

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Tunable LC Bandpass Filters- Part I & II

I’ve just completed Parts I and II of a design document for tunable bandpass filters using varactors. A number of helpful closed-form solutions are included. Link to Part I. Link to Part II.

RF and Microwave Design, RF Filter Design, Uncategorized Leave a comment

Using Companion Models for Time-Domain Simulation of ODE’s

Companion models can be used to quickly formulate the solution of simultaneous ordinary differential equations like those associated with analog circuitry. This approach is particularly helpful when this capability must be embedded in tools like MATLAB / SIMULINK / C++. The PDF file is located by following this link.

Digital Signal Processing, Mathematics, Software and Programming Leave a comment

CNC Router & Interview Questions

I have just added two new sections, one for my CNC Router related projects and a second one for interview related questions. Both are works in progress.

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Book chapter added on Direct Digital Synthesis

Extensive chapter added about Direct Digital Synthesis.

Digital Signal Processing, Frequency Synthesis Leave a comment

Updated Filter Design Documentation

Major revision to my filter design documentation 5.74 MB

Mathematics, RF Filter Design, Software and Programming Leave a comment

New Programming Projects 26Dec2012

Two new software/programming projects added. One for the design of lumped-element lowpass Butterworth, Chebyshev, and elliptic filters. The second for the design of resistive pi- and tee-pad resistive attenuators. Look at the bottom of the Projects page.

Software and Programming Leave a comment

New Book Chapter

I just posted a free book chapter on the site for anyone who has subscribed. The chapter is about 80 pages long and goes into a wide range of topics related to direct digital frequency synthesis (DDS). Definitely worth a read or a place in your reference material as this is not the same DDS perspective of years gone by.

The chapter is posted under the “More Articles” tab as the first article under the “Frequency Synthesis” category.

Digital Signal Processing, Frequency Synthesis Leave a comment

New Article in Microwaves and RF Out

My article in Microwaves & RF finally hit. The web version has a lot of typos in it, however, so you will probably find the PDF version a lot easier read. Follow this link and you’ll see the file link. Thanks for your interest.

Phase-Locked Loops (PLL), Uncategorized Leave a comment

New Article in May Microwaves & RF

I have a feature design article that is to be published in the May issue of Microwaves & RF. After it runs, I will post a copy of the complete article in PDF format for easier reading. The article presents several nonconventional methods that can help with demanding PLL designs.

Phase-Locked Loops (PLL), RF and Microwave Design Leave a comment

Approximation for RMS

Approximation for SQRT( I2 + Q2 ) with Gaussian Noise Present

When a complex signal is represented in terms of in-phase (I) and quadrature-phase (Q) components, a commonly used approximation for the signal root-mean-square (RMS) value is

Assuming a large number of OFDM subcarriers in the intended application, I and Q appear to both be Gaussian thereby making r a Rayleigh-distributed random variable where

We are interested in the ratio

From symmetry, it suffices to consider a limited range for θ as π/4 . Letting

leads to


where γ = 0.375. It is worthwhile evaluating just how good this choice for γ really is. We seek then to minimize the mean-square error given by

To read the article in its entirety in PDF format, please follow this link.

Digital Signal Processing, Mathematics Leave a comment

Computing Data Windows Recursively

Data windows are indispensable for computing the spectral characteristics of signal waveforms that are not periodic in time. In the context of hardware-based digital signal processing, most if not all data windows are expressed in terms of fairly complex function that are not convenient for embedding in a FPGA or custom ASIC. This memo presents several simple recursive results that can be used to compute these windows without excessive memory requirements and computationally intensive functions. The techniques described here can also be extended to other windowing functions as well.

This paper is offered for sale here.

Digital Signal Processing, Mathematics, Uncategorized Leave a comment


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Dreaded Interview Questions Just for Fun- Part I

James A Crawford

Having reached a sufficient station in life that I have either heard most of the typical interview questions that might come my own direction, or have the wit and nonsense to navigate my way through something that I don’t know and talk about the weather or something completely unrelated, this on-going collection of (technical) interview questions is intended just for fun. I encourage any readers to forward me their own most favorite technical questions at jk@am1.us. Don’t get up-tight though, after all, this is just for fun.

Question #1:

What is the equivalent of jj ?

This is very straight-forward to solve if we first write the base j value as j = exp( j π/2 ) based on Euler’s formula. Given that substitution, then

Dreaded Interview Questions Equ 1

Question #1B: Corollary to #1

What is the equivalent form of

Dreaded Interview Questions Equ 2

This is the same as Question #1 except it has been re-cast in a slightly different form. The progression from this form back to Question #1 is given by

Dreaded Interview Questions Equ 3

Question #2: In honor of Al Thiele

Solve for (x,y) in the set of real pairs with xy given xy = yx

From this starting point, clearly

Dreaded Interview Questions Equ 4


Dreaded Interview Questions Equ 5

In order to have a solution with xy, the quantity z = x / ln( x ) must be multi-valued along the real line. A rough sketch of the solution space can be found by collecting a bit more information.

Specifically, the slope dz/dx must approach infinity as x+ nears unity because the log function in the denominator will blow up. Similarly, a second derivative computation shows that the slope dz/dx with large x becomes

Dreaded Interview Questions Equ 6

It is also easy to show from this last equation that dz/dx= 0 for x= e.

Moving on to a complete solution to the problem, we can write

Dreaded Interview Questions Equ 7

where c is an auxiliary variable. Solving this equation leads to

Dreaded Interview Questions Equ 8

and substitution of this result back into y/x= c leads to

Dreaded Interview Questions Equ 9

From this result, it is easy to further conclude that

Dreaded Interview Questions Equ 10

The lesson here is to use simple graphical techniques to identify the behavior of a solution when possible. A picture is worth a thousand words.

Dreaded Interview Questions Fig 1 Dreaded Interview Questions Fig 2

The first part of these dreaded interview questions contains a total of 31 thought-provoking questions. To read further, just follow this link…

Frequency Synthesis, Mathematics, Phase-Locked Loops (PLL), RF Filter Design, RF System Design Leave a comment