About Ain

Analog and RF/Wireless integrated circuit and module design professional with over 38 years of experience in the industry. Worked for Fortune 500 companies for 18 years (Intel, ITT, Plessey and GTE. Currently employed by Signal Processing Group Inc.

Horn antenna

This post describes a methodology for the design of a pyramidal horn antenna. Following posts build on it and provide more details. A pyramidal horn is a popular antenna that has very little loss and is used commonly in antenna systems.  The structure of the pyramidal horn is shown in FIGURE 1.0 below.

Pyramidal horn structure

The design of a horn like this begins with a specification. Usually the following parameters are given:

Gain (in dBi)

a (inches or cm) (usually the horn is fed from a waveguide)

b (inches or cm) (usually the horn is fed from a waveguide)

frequency (Hz)

The problem is to find A and B, and other dimensions shown below. Once we have these dimensions, we can find other parameters of the antenna.

The usual procedure is to solve an equation to get a key parameter using the given specifications. This methodology will be outlined in this post and access to the equation solver will be provided. Subsequent posts will add more detail so that an engineer will be able to get a first cut design of the horn and fabricate it.

After the required key value is obtained through solving the equation the following steps are used to find the Horn parameters.


λ is the wavelength of the signal in cm. le is found from the solution of the equation.

Calculate B from this equation.

From B, λ, le and G calculate A. The equation to be used is:

G = (½)(4π/λ2)(AB)

Now we have A and B.

lh is found from the following equation:

A = sqrt(3λlh)

Calculate RH and RE from the following equation:

RE = (B -b)(sqrt[(le/B)2 – ¼)])

Since we are dealing with a pyramidal horn RE =RH

Use the following equation for R1:

lh2 = R12 + (A/2)2

Use the following equation to calculate R2:

le2 = R22 + (B/2)2

The equation to be solved is:
The quantity σ has to be solved for.
σ =le/λ . This equation is best solved numerically with a starting value of σ = G/2π√6. The Python program that was written to do this is available on request at spg@signalpro.biz or spg327@gmail.com

Ref: This blog is partially based on “Antenna Theory and Design, by Warren L. Stutzman and Gary A. Thiele. The book was published by John Wiley and Sons, 1981.
Ref: The Python program was written by Anuj Tripathi, University of Arizona, Tucson, Arizona.

Calculate the number of turns required for a given value of an inductor using a toroid.

Recently we published a calculator that provides the value of an inductor wound on a toroid given the number of turns of wire and other parameters.

A reverse calculator is provided now by SPG that calculates the number of turns needed to generate a given value of an inductor wound on a toroid. Please visit the SPG website and check under the “complementary” menu.

Calculate resistance of a semiconductor layer

A simple Javascript calculator for resistance of semiconductor layers.

The resistance of a resistive layer on an ASIC/IC is usually given (for hand calculations ) by taking the ratio of the length of the layer and its width and multiplying by its sheet resistance, (L/W)RS. Where L is the length, W is the width and RS is the sheet resistance. (Not every resistor can be calculated this way. Odd shapes are not amenable to this formula.) A simple javascript was generated at SPG that can be modified as needed to do this. Please visit the Signal Processing Group website to download the calculator free of cost. The calculator may be found under the “calculators” menu item.

Colpitt’s oscillator frequency calculator

A recent post presented the Colpitt’s oscillator starting point with a schematic and simulation results. In addition, it also provided a link to the recent book by Ain Rehman on this oscillator available from Amazon that contains design information and an exhaustive list of references for further study for interested readers. This post suggests downloading the Colpitt’s oscillator frequency calculator from the SPG website. It provides a good starting point and sanity check on the design of a Colpitt’s oscillator for the user. Please visit the SPG website and look under the ” Complementary” menu item.

3D printing for prototypes

3D design and printing has been gaining momentum recently for use in various applications — from microstructures to houses. Electronic enclosures and other parts are no exception. 3D design and printing is a quick way to make enclosures and fast prototypes using many different types of materials. The image below is a lighthearted print of a dragon. Be that as it may, if you want to print using a 3D printer please contact us for a bid as well. Please visit the SPG website for more information on our capabilities in electronics, ASICs and RF/Microwave modules.

Colpitt’s Oscillator book by Ain Rehman

A new book on the subject of the Colpitt’s Oscillator was just released on Amazon. This is a small book (text wise) but with an extended coverage of the subject for hands on work by engineers and students and other interested readers. It is very economical as far as the text and mathematical derivations go but supported by javascripts and a very extensive list of references that causes the virtual footprint of the book to be fairly massive. Interested readers may pick it up from
Colpitt’s Oscillator: Theory, design, simulation, references: Rehman, Mr Ain: 9798406680810: Amazon.com: Books

Vector Modulator

A vector modulator is a very versatile device that can be used to adjust the amplitude and phase of a RF signal. i.e it combines the functions of phase shift and attenuator. A vector modulator is a key component in 5G networks and can be used as a beamformer. It can be used in generating complex signals such as QPSK and QAM. It is also used in digital predistortion networks for RF power amplifiers. Please visit the Signal Processing Group Inc website for more technical information and articles.

Tf and fT relationship and calculations.

tf and fT are two closely related parameters for a bipolar model. Usually the parameter tf is included in the model and fT can be calculated from it and other parameters. tf is used to model the effect of the excess charge stored in the transistor when it is biased in the forward active region. i.e. the base – emitter junction is forward biased and the base collector junction is at 0 Volts. It is needed to calculate the emitter diffusion capacitance. fT is the transistor’s unity gain bandwidth defined as the frequency where the common emitter, zero load, small signal current gain extrapolates to unity ( Ref:”Modeling the bipolar transistor”. Ian Getreu). CAD programs use many different ways to use tf to convert to fT. However, this blog simply provides a way to get the conversion done to estimate the fT from tf. This provides the engineer a quick way to see what he may be dealing with without a lot of calculator overhead. If he needs a very accurate number he can always use an expensive simulator. This simple conversion is given by: fT(max)= 1/(2*pi*tf). This simple conversion assumes a zero value for the transistor’s internal collector pad to collector pin resistance. This resistance is assumed to be very small so this expression is a good estimate. Another assumption is that this is the maximum or peak value of fT. A calculator based on this expression is available from the Signal Processing Group website for download free of charge. Please visit the SPG website for other items of interest in analog and RFMW design.