# Analog to digital conversion

Updated: Aug 10

In all our homes, we are having a dish antenna television or at least we would have seen them in our friend's or relative's houses. Have you ever wondered how they are working? The antenna which has been fixed on the terrace of the house receives analog signals transmitted by the satellite. Then the analog to the digital signal conversion will be performed and the output can be viewed on the television screen.

Apart from this, the picture captured by a digital camera, the sound picked by a microphone is also the application of analog to the digital signal conversion process. This article briefly explains the concept behind the analog to digital conversion, the techniques involved, and the applications of this process.

### Analog to digital conversion:

**Analog **signals** **are kind of continuous signals for which the time-varying feature of the signal is a representation of some other time-varying quantity. (analogous to some other time-varying signal). Whereas the** digital** signal is the one which represents the data as a sequence of discrete values. Digital signals can take only a finite number of values in the given time.

The analog-to-digital converter(ADC) is nothing but a system that takes the analog signal as their input and converts them into digital signals. Due to complexity, most of the ADC architectures are implemented as metal-oxide based mixed-signal integrated circuits(ICs). This conversion process quantization of the input and so some noise has to be introduced.

**Bandwidth** and** signal-to-noise ratio**(SNR) are the two parameters through which the efficiency of ADC can be assessed. Bandwidth can be calculated by the sampling rate and SNR is influenced by factors such as aliasing, linearity, and resolution. This analog to digital conversion can be performed using different mechanisms. The most common technique is Pulse Code Modulation(PCM).

### 1.Pulse code modulation(PCM):

PCM involves three processes namely sampling, quantization, and encoding. High-frequency components in the input signal can be eliminated by using a low pass filter. This can also reduce the aliasing issue in the message signal. In PCM, the message signal is represented by a sequence of coded pulses. Sampling is the first process done in pulse code modulation.

### Sampling:

Sampling is a process of measuring the amplitude of a continuous-time signal at discrete instants, thereby converting the analog signal to a digital signal. To discretize a signal, the gap between the samples should be fixed. This gap can be termed as the **sampling period Ts**, which is inversely proportional to the sampling frequency. The sampling rate or sampling frequency denotes the number of samples taken per second.

**Ts=1/fs**

where fs is the sampling frequency. The sampling rate should be twice that of the highest frequency so that the data in the signal is not lost or overlapped. This rate of sampling is called a **Nyquist rate**.

**fs=2W**

where W is the highest frequency. A theorem called sampling theorem or **Nyquist-Shannon sampling theorem **was stated on the theory of this Nyquist rate. The theorem states that" a signal can be exactly reproduced if it is sampled at the rate **fs **which is greater than twice the maximum frequency **W**. There are almost three kinds of sampling. They are Ideal, natural, and flattop sampling.

In

**ideal**also called instantaneous sampling, pulses from analog signals are sampled. By taking Fourier to transform on both sides, the respective signal can be sampled. This kind of sampling cannot be implemented practically because pulse width cannot be zero and the generation of impulse trains is not practically possible.In

**Natural**sampling, the pulses possess a width which is equal to time period T. The resultant signal is a sequence of samples that retain the shape of the analog signal.In

**flat-top**sampling, the top of the samples remains constant by using a circuit. This is the most employed sampling method and much easier when compared to natural sampling.

### Quantization:

The process of digitizing analog signal rounding off the values which are equal to analog signal values. This sampling method chooses few points on the analog signal and they are joined to round off the value near to the stabilized value. This process is known as quantization.

The type of quantization in which the quantization levels are uniformly spaced is termed as **uniform quantization**. Whereas the quantization in which the relation between the levels is logarithmic and unequal is known as **non-uniform **quantization**. **The difference between the input value and the quantized value is known as quantization error. The device or algorithmic function which performs the process of quantization is known as **a quantizer.**

### Encoding:

After quantization, the digitization of the analog signal is completed by the process of encoding. **Encoding** minimizes the bandwidth used. It designates each quantized level by a binary code. After quantizing each sample, the number of bits per sample is calculated and changed to an n-bit code.

### 2.Delta modulation:

The above-discussed PCM is a complex technique. To reduce complexity techniques such as delta modulation, pipelining are introduced. The type of modulation in which the sampling rate is much higher and the value of step size is a smaller value (Δ) after quantizing is known as **delta modulation. **The Salient features of delta modulation are as follows,

To use the concept of signal correlation at maximum level, over-sampled input is taken. The quality of modulation is quite moderate but the design is pretty simple. The input sequence is much higher than the Nyquist rate. The bit rate of the output signal can be decided by the user and the implementation of this technique is also easy. As the sampling interval is reduced, the signal correlation will be higher.

The **modulator** is used at the sender part to create a stream of bits from the analog signal. while proceeding the process a small positive change called delta is recorded. If the value of delta is positive, then the process is recorded 1 otherwise it's zero.

### 3.Adaptive delta modulation:

In delta modulation, the value of step-size determines the quality of the output wave. In order to remove this query, **adaptive delta modulation(ADM) **has been introduced. If the message signal has a small slope, then a small step-size is required and for a steep slope, the condition is vice versa.

So the concept of **ADM** is controlling the step-size value according to our requirement so that the desired sampling output can be obtained easily. **ADM** quantizes the difference between the value of the current sample and the predicted value of the next sample.

### Applications of analog to digital conversion:

Some partial-electronic devices such as rotary encoders are also a kind of analog to digital converters. The rotary encoder is nothing but an electro-mechanical device that converts the analog position or motion to digital output signals.

All kind of sensors which measure temperature, pressure, light intensity, pH produce an analog signal. ADC helps us to convert these analog inputs into corresponding digital numbers.

Digital storage oscilloscopes require analog-to-digital convertors which can perform at a faster rate and also for software-defined radios.

Slow on-chip 8, 12, and 16-bit ADCs are employed in microcontrollers.

ADCs also play a crucial role in radio and television broadcast applications.