Click on the following bookmarks for further details of a Periodic Wave Tool for emc analysis: Fourier Analysis of
Trapezoid Waves
Digital waveforms with fast rise and fall times, which can be as little as a few ns, can be significant sources of radiated and conducted interference. An initial step in identifying the source of particular peaks in emissions for example is to consider the harmonic frequencies produced by suspect waveforms. Any time periodic waveform can be expressed as a series of discrete sinusoidal frequencies, occurring at multiples, or harmonics, of the original digital waveform. The Fourier analysis tool automates this analysis. The Fourier analysis data entry form is shown below. A spot analysis is available, in addition to a plot facility. Note that the number of harmonics to be plotted can be set; plotting time can be lengthy on 486 based computers if numbers much in excess of 100 are specified.
The data form for the Fourier analysis of a chopped sinusoidal waveform is shown below, and this is similar to the trapezoidal waveform analysis. Note that the number of harmonics to be plotted can be set; plotting time can be lengthy if numbers much in excess of 100 are specified.
Digital waveforms are found in an infinite variety of combinations of pulse patterns, perhaps comprising bursts of short pulses, or sequences of variable width pulses. The harmonic content of such pulse trains is more complex than that of a constant width rectangular waveform, and the Fourier Analysis: Pulse Sequence Tool allows analysis of the Fourier harmonics of a repeating sequence of up to 50 variable width pulses. The Pulse Sequence Tool is shown below:
Successive pulses are defined in terms of high, or on, time, and low, or off, time. The period and frequency of the entire sequence is calculated automatically from the sum of the individual pulse durations. Defined pulses can be deleted, and new pulses can be inserted into the sequence. The entire sequence can be deleted using the Clear All button. The Pulse Voltage defines the on voltage for all pulses, and the Rise Time and Fall Time defines those values for all pulses. Individual harmonics can be calculated using the Analyse button, whereby the actual harmonic value and its value relative to the Pulse Voltage is displayed. The Fourier spectrum can be displayed using the plot button; an example of a series of 5 pulses of 5 microsecond duration, with a sequence frequency of 1.835kHz is shown below: The Discrete Fourier Transform Tool can be used to obtain an
approximation to the Fourier transform of a User Defined Waveform. One cycle of the
waveform is defined either by pointing and clicking on the graph area, or by entering the
data points to a Table. The Table is accessed by the Table button.
The L-C filter shown below is used to illustrate the analysis principle used in the emi suppression filter tool. Inductors are represented as a series inductor and series resistor, shunted by a capacitor Cs to represent self-capacitance. Capacitors are represented as an ideal capacitance in series with an inductance and resistance. For feedthrough filters, Le can be taken as being practically zero, whilst the residual resistance Rc is typically 5 mohms in value. The inductance Le dominates the rf performance of leaded capacitors, and is due to construction and lead inductance. A typical value of 5nH produces a significant resonance in the insertion loss characteristic. The EMI Suppression Filter Data entry form. Insertion loss, the basic assessment of emi suppression
filter performance is defined as the ratio of the voltage across the load Rl before
addition of the filter to the voltage across Rl after the addition of the filter.
(Expressed in dB). Insertion loss plot of a 10nF capacitor, in various
impedance systems. Curve 2 shows the conventional 50 ohm source and load. Curve 3 shows
how the capacitor performs between a 5 ohm source and load, where insertion loss at any
particular frequency is much reduced. Curve 1 shows the increased loss when the system
source and load impedance is increased to 500 ohms. Curve 1 depicts a 100nF capacitor with no ground inductance; this plot would be typical of a feedthrough capacitor. Curve 2 shows a 100nF capacitor with 5nH of ground inductance, such as may be obtained with a leaded capacitor. The Common Mode Choke consists of two inductors wound
on a common core (often toroidal), and is used, as the name suggests, to suppress common
mode noise. The windings are arranged so that flux due to the differential mode signal
currents cancel out, and a low insertion loss is offered to normal signal currents. The signal insertion loss will also be increased below the cut-off frequency. The CM Choke tool also calculates and plots the ratio of the noise voltage at the load to the common mode noise voltage in the ground loop. The cut-off frequency again determines whether or not any common mode noise reduction occurs. Below the cut-off, no attenuation occurs. The Common Mode Choke data form. Three different types
of plot are provided. Low frequency signal insertion loss for a 1mH common
mode choke. The insertion loss is constant above a cut-off frequency, determined by the
series resistance and the choke inductance. Curves 1 to 5 show the effect of increasing
the resistance from 1 ohm through to 15 ohms, each increase in resistance raising the
minimum frequency where the choke is effective. The insertion loss itself is entirely due
to the series resistance, not the inductance. The ratio of the noise voltage at the load to the noise voltage in the ground loop is plotted below, for the same parameters as used in the graph above. The circuit for the noise voltage analysis is also shown below. This plot shows that the there is little or no
attenuation of common mode noise below the cut-off frequency. A collection of common mode current insertion loss
plots for a common mode choke with varying self-capacitances. These range from 1pF in
Curve 1 to 15pF in curve 5, all for a constant choke inductance of 1mH. This tool offers a range of conversions around the decibel ratio, using the form shown below: A decibel (dB) is the unitless logarithmic ratio of two quantities,
and may be expressed as: |

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