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GATE EC 2021 Official Paper

CT 1: Ratio and Proportion

2672

10 Questions
16 Marks
30 Mins

__Concept:__

**To avoid slope overload:**

\(\frac{{\rm{\Delta }}}{{{T_s}}} ≥ 2π \;{A_{max}}{f_m}\)

\(T_s=\frac{1}{f_s}\)

Δ × f_{s} ≥ 2π × A_{max} × f_{m }---(1)

Where,

Δ = Step size

Ts = Sampling interval

f_{s} = sampling rate

Amax = Maximum amplitude of message signal

fm = Message signal frequency

__Calculation:__

**Given:**

f_{m} = 4 kHz

f_{s} = 32 kHz

A_{max} = 4 V

Using equation (1) we can calculate the minimum step size:

Δ × 32 ≥ 2π × 4 × 4

\({\rm{\Delta }} ≥ \frac{2π}{2}\)

Δ ≥ π

**Δ ≥ 3.14**

__Important Points__

__Delta Modulation (DM)__:

It is used to reduce the bandwidth or bit rate.

1. It is considered a 1-bit DPCM. So, the encoder is a 1 bit ADC, i.e. only 1 sample is used in DM.

2. The encoder output is either 1 or 0

3. Two quantization levels are used + Δ and - Δ.

Two types of distortions (Errors) occurs in Delta modulation system i.e.

1) Slope overload error

2) Granular Error

This is explained with the help of the given figure:

** **