**PULSE & DIGITAL CIRCUITS**

UNIT-
I

**LINEAR WAVE SHAPING :**High pass and low pass RC circuits and their response for sinusoidal, step, pulse, square wave, ramp and Exponential inputs, RC network as a differentiator and integrator, attenuators and its applications in CRO probe, RL and RLC circuits and their response to step input, ringing circuit.

**Important Points to REMEMBER:**

A

A

A linear network can be applied with sinusoidal or non-sinusoidal input.

If a sinusoidal input is applied to a linear network, then the response (output) of the network is also sinusoidal except a change in magnitude and/or phase in the output waveform. ie. Linear circuit does not alter the shape of sinusoidal input signal.

When a non-sinusoidal signal is applied to a linear network, then output will be distorted ie. Output signal is different from input signal.

Examples of Non-sinusoidal signals are Impulse, Step, Pulse, Square, Ramp, Exponential etc....

Def :

The function of capacitor is to store energy in the form of electric field, which is proportional to voltage. In general, capacitor charges when a current flows into it and while capacitor discharges, current flows out of the capacitor.

When a DC or step voltage is applied, capacitor charges exponentially to the final value from initial value based time constant of the circuit.

Time constant (τ) is the product of equivalent resistance and equivalent capacitance across the terminals of interest (τ = RC). Units of time constant are seconds.

In one time constant of time, capacitor either charges / discharges to 63.2% of the final value. Capacitor requires a minimum of five time constants of time to charge / discharge to the final value. Hence small the time constant , faster the response of the circuit.

Risetime (t

LPRC circuit works as Low Pass Filter, which passes all the frequencies starting from DC (0 Hz) to upper 3dB frequency (f

Bandwidth and rise time are related as BW * t

LPRC circuit works as integrator if time constant of the circuit is very large compared to duration of the pulse.

For Integrator, if the input is Impulse then the output is Step (or) if the input is step then the output is Ramp (or) if the input is Ramp then the output wave shape is parabola.

**linear circuit**is one which consists of only linear elements. Examples of Linear elements are R, L and C.A

**Non-Linear network**is one which should at least contain one non-linear element, along with linear elements. Examples of non-linear elements are Diode, BJT, FET, SCR, UJT, DIAC, TRIAC etc...**Response of Linear Networks :**A linear network can be applied with sinusoidal or non-sinusoidal input.

If a sinusoidal input is applied to a linear network, then the response (output) of the network is also sinusoidal except a change in magnitude and/or phase in the output waveform. ie. Linear circuit does not alter the shape of sinusoidal input signal.

When a non-sinusoidal signal is applied to a linear network, then output will be distorted ie. Output signal is different from input signal.

Examples of Non-sinusoidal signals are Impulse, Step, Pulse, Square, Ramp, Exponential etc....

Def :

**Linear Wave Shaping**: is the study of variation in output signal of linear network, when applied with non-sinusoidal signals.The function of capacitor is to store energy in the form of electric field, which is proportional to voltage. In general, capacitor charges when a current flows into it and while capacitor discharges, current flows out of the capacitor.

When a DC or step voltage is applied, capacitor charges exponentially to the final value from initial value based time constant of the circuit.

Time constant (τ) is the product of equivalent resistance and equivalent capacitance across the terminals of interest (τ = RC). Units of time constant are seconds.

In one time constant of time, capacitor either charges / discharges to 63.2% of the final value. Capacitor requires a minimum of five time constants of time to charge / discharge to the final value. Hence small the time constant , faster the response of the circuit.

Risetime (t

_{r}) : is the time required for the waveform to reach from 10% to 90% of its final value. Rise time for a simple RC circuit is equal to 2.2RC.LPRC circuit works as Low Pass Filter, which passes all the frequencies starting from DC (0 Hz) to upper 3dB frequency (f

_{H}). Bandwidth of LPRC circuit is equal to f_{H}.Bandwidth and rise time are related as BW * t

_{r}= 0.35LPRC circuit works as integrator if time constant of the circuit is very large compared to duration of the pulse.

For Integrator, if the input is Impulse then the output is Step (or) if the input is step then the output is Ramp (or) if the input is Ramp then the output wave shape is parabola.