# Analog Signal Processing Circuits

Let us look at an example application of Analog Signal Processing for looking at its typical steps.

Consider a simple microphone-amplifier-speaker setup, which aims at listening to speech signal, amplifying it and and then reproducing it via speakers.

#### Example of ASP

- Generation of Analog Signal : This is done using transducer, which converts from one form of energy to another. Here, Microphone is a transducer which converts acoustic energy to electrical energy (voltage waveform).
- Amplification: It increases the power-level of the input waveform. In general, amplification involves multiplying a signal by a constant factor, k.
- k<1 implies Attenuation
- k>1 implies Amplification
- k=1 implies Buffer

- Output: Speaker emits sound as output.

While amplification, if we obtain the exact replica of the input at the output of amplifier, we call it having ‘no distortion’. But if we obtain the exact replica after a lag, we say to have obtained it after a ‘time delay’. Practically, we aim for no distortion with least possible delay.

While testing amplifier, we may need a certain set of test signals to check its performance.

#### Test Signals:

- Sinusoidal Signal : Vpsin(wt) , where Vp is the peak voltage (Volt), w is the frequency in rad/s
- It is the most widely used test signal because any periodic signal can be represented as a weighted sum of sinusoids (Fourier Series). Hence, behavior of a circuit upon a periodic excitation can be predicted from its behavior upon a sinusoid.

- Trigger Pulses : Periodic pulse train with each spike separated by an equal time interval T.
- Square Wave
- Triangular Wave

**Signal Shaping Circuit**:

- Clippers
- Clampers

**Multiplier**

It is the basis for mixing, modulation, demodulation in communication systems.

V_{o}= V_{x} . V_{y} / V_{R}

**Divider**

V_{o}= V_{x} . V_{R} / V_{y}

##### To summarize, the circuits for ASP, which we will be covering include:

- Amplifier
- Signal generator (oscillator)
- Signal Multiplier
- Wave shaping circuits
- Amplitude (AM) and Frequency (FM) modification

V_{p} sin w_{c}t =====> AM ======> V_{m} sin w_{m}t sin w_{c}t , done using multiplier

V_{p} sin w_{c}t =====> FM =======> V_{p} sin[ w_{c}t + del(w_{d}) sin w_{m}t ]t, done using Voltage Controlled Oscillator (VCO).

**Elements in Analog Signal Processing**

- Resistor , R
- Capacitor, C
- Inductor, L

R, L, C are passive, linear and bilateral two-terminal elements.

*Linearity: *By its definition, a device is linear, if the linear sum of the inputs into it yield the linear sum of corresponding outputs.

Excitation, V and the response, I across a resistor R, follow a linear relation given by : I = V/R

For a capacitor, V / I = 1/ jwC, which implies an inverse proportional relation under a fixed frequency w.

For an inductor, V/I = jwL, which implies a direct proportional relation between V & I under fixed frequency w.

*Bilateral: *Current can flow across these elements in either direction based upon the voltage polarity.

4. Diode, D

It is a unilateral, non-linear, passive two-terminal device.

*Unilateral: *Current flow is possible only in one direction, i.e., for forward biasing only.

*Non-linearity:*

Forward biasing: i>0 => V=0 =>R=0…..Diode acts as short circuit.

Reverse biasing: V<0 => i= 0 => R= inf….Diode acts as open circuit.

Hence, V-I characteristic of ideal diode is piecewise-linear. Thus, called non-linear.

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