# PRBS signal power calculations using sinc squared function integration

The power in a PRBS NRZ signal is expressed as a sinc squared function of the independent variable x. In order to calculate the power in this signal from 0 to some arbitrary x a definite integral of the sinc squared function has to be found. This is not an easy task. Having searched the web for ready solutions of this problem very few relevant references were found. Therefore a technique was evolved from series expansions of the sinc and sinc squared functions. The accuracy of the estimates found by using this technique is completely dependent on the engineer. We found that using just four or five terms in the expansion allowed us to calculate to within accuracies of interest to us. The technical report can be found in the engineer’s corner in the SPG website located at http://www.signalpro.biz.

# Analog and mixed signal design:Input impedance of a common emitter bipolar differential amplifier with emitter degeneration

Use of the emitter coupled bipolar differential amplifier is prolific. In addition a good way to stablize gain and bias stability is the use of a emitter degeneration resistor. This post simply presents, without proof, what happens to the input impedance of the differential device when degeneration is used. First one has to know the rpi of the bipolar small signal model. This is calculated as: Beta0/gm. Where Beta0 is the dc gain of the bipolar. If no degeneration is used, this is the input impedance of the transistor. When a degeneration resistor is used then the impedance rises significantly. The rise in input impedance is: (Beta + 1)*Re. Here Beta is the current gain at the particular bias point and frequency and Re is the degeneration resistor. Therefore the total input impedance rises to rp1+(Beta+1)*Re. For other items of interest please visit our website at http://www.signalpro.biz.

# Dot rule for transformers

The dot rule for transformers is a convention used to present the voltage and current relationships and phase. It is a simple rule and therefore sometimes easy to forget, if not used every day. In order to use this rule we need to know two things: (1) The right hand rule for current and fluxes. i.e. If the fingers of the right hand are wrapped around the core in the direction of current flow, then the thumb will point in the direction of the flux. (2)If the current enters a dotted terminal, it causes a positive voltage at the other dotted terminal.If a current leaves a dotted terminal, it induces a negative voltage at the other dotted terminal. For more technical articles and items of interest please visit our website at http://www.signalpro.biz.

# Adjacent channel power ratio ( ACPR)

In multicarrier systems, the carriers can be spaced quite close to each other. When this is the case a quantity referred to as the adjacent channel power ratio or ACPR becomes important. As mentioned above, multicarrier systems have a number of carriers which may generate signals whose power may add in phase. As more tones or signals start interacting, the peak additive power will increase. The average power of these signals may well be within the dynamic range of the system. However, the peaks of power may exceed the dynamic range. This will cause non linear odd – order distortion in the system. When this happens it results in adjacent channel power output or ACP. The ACPR is the ratio of the system output power at an offset frequency with respect to the power of the channel of interest. This can be considered one measure of linearity of a transmitter ( or RFPA). If the transmitter or the PA generates unwanted sidebands at an offset frequency that lies within the passband of an adjacent channel. For a given modulation scheme, the relationship between third order intermodulation products and the ACPR at a given power level is: ACPR = IMR2-tone + 10*log[ n**3/(16X + 4Y)].For a given modulation scheme, the relationship between third order intermodulation products and the ACPR at a given power level is: ACPR = IMR(2-tone) + 10*log[ n**3/(16X + 4Y)]. Here X and Y are given by:

X = (2n**3 – 3n**2 – 2n)/24 + [mod(n/2)]/8.0

And

Y = n**3 – {[mod(n/2)]/4.0}

All ratios here are in dBc. i.e. the ratio of the two tone intermodulation to signal carrier IMR and ACPR. Check out our website and engineer’s corner. Go to http://www.signalpo.biz.

# Random signal generation for PSPICE/SPICE

The SPICE programs we use for circuit simulation do not have a direct way to generate random waveforms. i.e. there is no voltage or current source which can be attached to a circuit node and which can generate a random signal for analysis. As a result we had to develop code on MATLAB and C++ to allow us to generate a PWL random waveform of as long a length as required. It is used as a piece wise linear signal and can generate the random signal as required.Please contact us through our website located at http://www.signalpro.biz for more information about this circuit simulation tool.

# Decimation filters for Sigma – Delta A/Ds

A typical filter used as the pre-decimation filter for an oversampled A/D is the Hogenauer filter, also called the CIC filter. These filters have some advantages which make them particularly suitable for use as decimation filters. In general the output stream from a OSR A/D is a 1 bit high frequency digital signal. The 1 bit signal has to be downconverted in frequency and increased in bit width. This is the fundamental decimation operation. Hogenauer filters offer the following advantages (1) No multipliers are needed. (2) No storage is needed for filter coefficients. (3)Intermediate storage is reduced by integrating at the high sampling rate and comb filtering at a low rate. (4) The structure of the CIC filters is very uniform, using only two basic building blocks. (5) Little external control or complicated local timing is required. (6) The same design can easily be used for a wide range of rate change factors with the addition of a scaling unit. As a result of these advantages Hogenauer filters have been used and continue to be used in overampled systems. A technical report prepared by technical staff at Signal Processing Group Inc. is now available in a series of posts that deal with the Hogenauer filter as well as OSR A/D converters. It was assumed that since the CIC filter is an important component at the backend of an OSR ADC, understanding the design parameters of this filter is essential to the design of the overall OSR ADC. Subsequent posts to this one deal with the details of design for decimation filters. The paper may be found at http://www.signalpro.biz>engineer’s corner.