Minimizing Distortion and Noise in a Pulse-Width Modulated Transmission

This application note is a technical guideline intended to reduce the amount of noise added to field measurement from a transducer via a transmitter to a receiver that is acquiring the transmission. This instruction is meant for applications where the transmitter has encoded the field measurement using pulse-width modulation and is driving a transmission line with a signal to be measured by a receiver at a remote location. The discussion herein was modeled for instances where transmission is necessary through an industrial setting where interference from very high voltages is not uncommon. The transmission line implemented herein is a standard shielded twisted pair line. BACKGROUND For telecommunication purposes, the utility of pulse width modulation (PWM) lies within the duty cycle of the encoded signal. Like frequency modulation, PWM has inherent noiseimmunity that permits an analog signal to be sent on a relatively lengthy wire-line communication channel with minimal interference. The amplitude assumes one of two relatively discrete values similar to digital communication; thereby the noise has to be significant enough to change the switching of the states. However, as the length of the transmission channel increases, the probability of outside interference affecting the signal integrity also increases. Noise and distortion can compromise the function of PWM by skewing the duty cycle and altering the wave shape of the pulse. DISTORTION Distortion for a PWM waveform is a direct function of the transmission channel. For a given step function, the rise time of the pulse edge will increase as the cable length increases. Since a pulse is composed of several harmonics of sine functions, the high frequency components of the pulse will have the highest susceptibility to attenuation and delay. If the frequency of the transmission exceeds the bandwidth of the channel, significant distortion will occur. Figure 1 – Example of Distortion of a Pulse Edge with Increased Cable Length [2] COMMON NOISE SOURCES There are many different mechanisms for generating noise within a circuit. The basic principle involves a noise source that interacts with a circuit via a coupling method. [1] It is virtually impossible to have a noise-free circuit; however by understanding the phenomena of noise and distortion, measures can be taken to minimize their impact on critical parameters of the overall design. Thermal Noise It is the most prevalent source of noise within a circuit and is due to the thermal agitation of electrons within a conductor and is a primary contributor of “white noise” within a circuit. It is often associated the noise generated by resistors within a circuit. Therefore the non-ideal resistor can be modeled as a noise voltage source in series with an ideal resistor. It can be characterized by the following relationship: = kTBR [ ] k= 1.38x10 -23 J/K (Boltzman’s Constant) T= Temperature in degrees Kelvin B= Noise bandwidth R= Resistance [3,6] Shot Noise A source of noise with minimal impact on a circuit, it is due to the random fluctuations in a DC current due to the discrete nature of charge carriers within a conductor. It is often a phenomena associated with transistors. It can be represented by the following equation: = 2 [ ] g= 1.6x10 -19 Coulombs (electron charge) = DC current B= Noise bandwidth [3,6] Flicker Noise Surface defects, contamination and other imperfections often can create traps for charge carriers to accumulate. Flicker noise is the characterization of the random emission of electrons associated with these imperfections. However unlike “white noise” that has a flat power spectral density over all frequencies, flicker noise has frequency dependence. This occurs in active devices or carbon resistors, and can be characterized by the following equation: = [ ] = Flicker coefficient f= Frequency a= Flicker exponent (default=1) B=Noise bandwidth [3,6] Burst Noise (Popcorn Noise) This source of noise is quite similar to flicker noise in that it is due to contamination and other imperfections that lead to carrier traps, with the exception of the magnitude and mode of emission of the charge carriers. Often heavy ion implantation can lead to these defects. The step-like transitions create a popping often associated with audio speaker noise. The relationship can be exhibited by the following equation: