18-12-2012, 03:02 PM
Linear Waveshaping
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Introduction to Linear Waveshaping
In a linear circuit, all components are assumed to be operating within their
respective linear regions.
Linear circuits preserve shape of a sinusoidal signal, and alter shapes of nonsinusoidal
signals.
Linear Waveshaping is the process by which a non-sinusoidal signal is altered
by transmission through a linear network.
Presented by APN Rao, Dept ECE, GRIET, Hyderabad. Jan 2012 2
Responses of simple RC, RL and RLC circuits to some standard input
waveforms will be studied in this unit.
Modelling R, L, C: Inferences
In a resistor
Voltage and current are always in time phase.
Voltage decreases in the direction of current.
In a capacitor
Voltage varies as time-integral of current. Constant charging current produces linearly varying
voltage.
Voltage across a capacitor can not change discontinuously for finite-valued currents.
Presented by APN Rao, Dept ECE, GRIET, Hyderabad. Jan 2012 4
Open circuit (infinite impedance, zero current) to dc voltage and short for high frequencies
In an inductor
Current is time-integral of voltage. Constant voltage produces linearly varying current.
Current through an inductor can not change discontinuously for finite-valued voltages.
Short circuit (zero impedance, zero voltage drop) to dc current and open circuit to high
frequencies.
How small should be RC for a good differentiator?
High Pass RC Circuits
Think of input waveform approximated satisfactorily by straight-line segments,
making it a step-ramp construction using suitably sized time-intervals. For good
differentiation, RC should be much smaller than the smallest of those timeintervals.
Sinusoidal response of an ideal differentiator is also a sinusoidal wave with 900
phase lead. A practical circuit provides a phase lead = tan-1(1/ωRC), which is less
than 900. Better the differentiation, closer would be the phase-lead to 900. A
criterion for good differentiation is to specify the minimum phse-lead as 89.4o.
This implies ωRC < 0.01, at the frequency corresponding to the smallest time
Presented by APN Rao, Dept ECE, GRIET, Hyderabad. Jan 2012 15
interval of appreciable variation (ω=2π/T).