# A note from the editor:

*We are always so impressed by how generous the maker community is. From the endless amounts of open-source projects to electronics enthusiasts wanting to share their knowledge with others. This month, we were contacted by one such maker who wanted to share his knowledge about pulse code modulation. Elmo has published several articles in Australian Electronic Magazines and has self-published a book titled ‘Amplitude and Frequency Modulation Basics - A Programmed Instruction Unit’. Here’s what Elmo had to say about pulse code modulation.*

Pulse Code Modulation or PCM sometimes referred to as Digital Modulation is a communications system in which analog signals (The ones we are familiar with) are converted into digital or binary form for transmission.

Analog signals suffer from distortion and noise problems but are used as a preliminary step in the generation of PCM.

In PCM, the sample value is converted into a segment of binary data and then transmitted. Since binary codes depend only on the absence or presence of a binary digit, the pulse height, width, or energy level of the pulse does not affect the information.

It is relatively easy to recover the pulses even under noise and distortion. This makes PCM very useful for long distance communications.

# PCM Steps

The following steps are required in a PCM system:

- The message is sampled at regular intervals.
- The sample value is represented by an n digit binary number. The number of digits used depends on the application. More digits give a more accurate received value.
- The binary number is transmitted to the receiver as a segment of a binary waveform.
- Steps 2-3 are repeated for successive samples.

The sample values are represented by the vertical lines and the horizontal grids are the allowed values. The transmitted pulses have values 0 through to 15 volts. In the figure, the sample value has a value X which lies between 6 volts and 7 volts.

If the system uses rounding down, the value of X is transmitted as 6 volts. That is 0110 using 4 binary digits. If rounding up is used, X is transmitted as 7 volts which is 0111 in binary. Assuming we are still using four binary digits.

The following definitions are used in PCM systems:

- Quantization – the process of representing analog pulses by certain discrete values.
- Quantization Error – The error between the received sample value and the actual sample value.
- Quantization number – The effect of a succession of quantization errors.
- Quantization levels – The horizontal lines in the figure.
- Quantization intervals - The spaces between the horizontal lines.

**A note from the editor:** All values that are measured by such a system like this are impossible to capture entirely. When you measure "9.01V" on your multimeter, the value may really be "9.01251258513513...." off to infinity. This is because values like voltage, time, temperature, etc. are continuous, not discrete, by nature. We can't quantise these values on paper or define them without cutting off the significant figures somewhere. So, this is what we call quantisation. When we say the value is 9.01V, we have quantised it. Our multimeter has done this for us. The error between 9.01V and the real value is an example of a quantisation error.

# Bandwidth of the PCM signal

The bandwidth of the PCM signal is given by – Bandwidth = ½ the rate at which the digits are generated by the PCM modulator.

# Signal to Noise Ratio

The signal to quantization noise ratio produced by a PCM encoder and decoder using n bits for a sinusoidal signal is given by the equation:

S/N = (6n + 1.8) dB

Let us make n=1 and 2 and see what this equation yields.

When n = 1, S/N = (6 + 1.8) = 7.8dB

When n = 2, S/N = (12 + 1.8) = 13.8dB

The difference is 6dB, which is another way of saying that for every extra pulse used, the signal-to-noise ratio increases by 6dB.

Unfortunately, sending more bits in the same time increases the bandwidth. If bandwidth is at a premium, no more digits should be used than are necessary to achieve the signal to quantization noise ratio for the transmitted signals.

# Sampling Rate

The sampling rate is also called the Nyquist Sampling Rate.The minimum sampling rate is equal to twice the highest frequency contained in the signal. Telephone speech can have frequencies up to 3400 Hz. The telephone signal would have to be sampled at 6800 samples/sec. to satisfy the Nyquist sampling rate. A rate of 8000 samples/sec. is generally used.

Let us now determine the sampling rate required for a signal extending from 0 to 3kHz, the bit rate for a 7bit PCM signal to encode this signal, and the minimum bandwidth required.

- Using the Nyquist rate, the minimum sampling rate
- = 2 x the bandwidth
- = 2 x 3000 = 6000 samples/sec
- The Bit Rate = 7 x 6000 = 42000 bits/sec.
- The Minimum Band Width = ½ the bit rate = 21,000 Hz.

The sample/hold circuit stores the value of the message until commanded to store a new value. Quantization occurs at the A to D converter. The total range that the message signal covers is divided into a number of standard levels. The A to D converter determines the quantum value of the sample and assigns a voltage value to it. The coding occurs in the A to D and parallel to serial converter. The converted data is the PCM signal.

The serial to parallel converter converts the signal into a series of parallel bits which go through a register and a D to A converter and is then applied to the low pass filter which extracts the original message signal.

# Companding

Up to this point, we have looked at encoders that use equal size intervals. These are called uniform encoders. This is unsatisfactory in some cases, such as speech signals from various speakers, for example. These can have a range of about 30dB. Most conversations take place at low levels and the upper end of the encoder is used only momentarily for loud talking or shouting.

One method is to use a non-uniform encoder that uses smaller step sizes for low level signals. Another method is to apply the signal to an amplifier with a non-uniform input/output characteristic, called a compressor, before coding (Figure.4).

After decoding, the signal is applied to a circuit with a complementary input/output characteristic called an expander (Figure.5). The combined compressor/expander is called a Compander.