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Have you ever wonder how signals travel in a telephone line?

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MODULE 14

PULSE CODE MODULATION

Prepared by:Engr. Jo-Ann C. Viñas

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OBJECTIVES:

1. Discuss the concept of digital transmission

2. Review the Pulse Modulation Theory and the parameters of PCM

3. Discuss the process of producing PCM

4. Apply sampling theorem and quantization to the PCM process

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DIGITAL TRANSMISSION

– is the transmission of digital signals between the transmitter and receivers and requires physical transmission medium such as cable, fiber optic , etc.

Transmitter

Transmission Medium

Receiver

Digital Information

ADC

Analog Information

Wire, cable, fiber optic, etc

DAC

Analog Information

Digital Information

ADC – Analog to Digital ConverterDAC – Digital to Analog Converter

DIGITAL TRANSMISSION

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DIGITAL TRANSMISSION ADVANTAGES

1. Noise immunity

2. Better suited to processing and multiplexing

3. Uses signal regeneration than signal amplification

4. Simpler to measure and evaluate

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1. Requires more bandwidth

2. Need for additional encoding and decoding circuitry

3. Requires precise time synchronization between transmitter and receiver

4. Incompatible with existing analog facilities

DIGITAL TRANSMISSION DISADVANTAGES

PULSE MODULATION

- The process sampling an analog information signals and then converting those samples into discrete pulses and transporting the pulses from a source to a destination over a physical medium.

PULSE MODULATION

- The process of using some characteristic of a pulse (amplitude, width, position) to carry an analog signal.

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1. PULSE AMPLITUDE MODULATION

- Amplitude of the modulating signal changes the amplitude of the pulses (information)

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STEP 1: PAM PROCESS

Signals to be Mixed

pulse train modulating signal

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STEP 2: PAM PROCESS

Pulse Amplitude Modulation

pulse AM signal modulating signal

- A process where the pulse width of a fixed amplitude pulse varies proportionally to the amplitude of the analog signal.

2. PULSE WIDTH MODULATION

time

FIGURE 2: PWM SIGNAL

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3. PULSE POSITION MODULATION

- A form of pulse modulation where the position of a constant width pulse within a prescribed timeslot is varied according to the amplitude of the modulating signal

FIGURE 3: PPM SIGNAL

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- The process of transmitting analog information in digital form, which involves sampling the analog signal and converting the sampled to a digital number

4. PULSE CODE MODULATION

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PULSE MODULATION

WHERE:• Analog Signal• Sample Pulse• PWM• PPM• PAM• PCM

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SIMPLEX PCM TRANSMISSION

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PCM TRANSMIT BLOCKS

PCM DECODER

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STEPS TO PRODUCE PCM

1. Sampling2. Quantizing3. Encoding

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BANDLIMITING

- The anti-alias or bandpass filter limits the frequency of the input analog signal to the standard voice frequency band of 0 to 4 kHz.

PURPOSE: is to eliminate any unwanted signal that will result to aliasing or fold over distortion at the receiver.

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1. SAMPLING

- The act of periodically holding a value (sample) of the continually changing analog input signals.

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TYPES OF SAMPLING

1. Natural Sampling (Gating)

2. Flat-Top Sampling

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A. NATURAL SAMPLING (Gating)

The natural sampling method retains the natural shape of the sample analog waveform

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FIGURE 4: NATURAL SAMPLING

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B. FLAT-TOP SAMPLING

The most common method used for sampling voice signals in PCM where the sample-and-hold circuit convert those samples to a series of constant-amplitude PAM levels.

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FIGURE 5: FLAT-TOP SAMPLING

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FIGURE 6: SAMPLE AND HOLD CIRCUIT

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FIGURE 7: INPUT AND OUTPUT WAVEFORMS OF SAMPLE AND HOLD CIRCUIT

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EXAMPLE

For the sample and hold circuit, determine the largest value capacitor that can be used. Use an output impedance for Z1 of 10 , an on resistance for Q1 of 10 , an acquisition time of 10 sec, a maximum peak to peak input voltage of 10V, a maximum output current from Z1 of 10mA, and an accuracy of 1%.

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- States that for a sample to be reproduced accurately at the receiver, the sampling frequency must be at least twice of the highest modulating signal.

fs ≥ 2 fm

where:

fm= highest modulating signal

fs = sampling frequency

NYQUIST SAMPLING THEOREM

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FIGURE 8: OUTPUT SPECTRUM OF SAMPLE AND HOLD CIRCUIT

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3-BIT PCM CODE

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SIGN MAGNITUDE CODES

The codes currently used for PCM, where MSB is the sign bit and the remaining bits are used for magnitude

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- The codes on the bottom half of the table are a mirror image of the codes in the top half, except for the sign bit.

FOLDED BINARY CODE

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3-BIT PCM CODE

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- the magnitude difference between steps

QUANTIZATION INTERVAL

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FIGURE 9

where:

a. Analog input signal c. PAM

b. Sample pulse d. PCM

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FIGURE 10

where:

a. Analog input signal c. PAM signal

b. Sample pulse

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EXAMPLE

For a sample rate of 20 kHz, determine the maximum analog input frequency.

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EXAMPLE

Determine the alias frequency for a 14 kHz sample rate and an analog input frequency of 8 kHz.

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- The process of assigning discrete level to time-varying quantity in multiples of some fixed unit, at a specified instant or specified repetition rate.

- Is the process of approximating sample levels into their closest fixed value

2. QUANTIZATION

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QUANTIZING BY USING SIGN AND MAGNITUDE

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- The quantized levels are those fixed levels that are the nearest to f(s) at the point the sample is taken.

QUANTIZATION ERROR/NOISE

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QUANTIZATION ERROR

Qe =Vmin

2

Qe

Resolution=

2

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LINEAR INPUT VS.OUTPUT TRANSFER

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- The magnitude of a quantum.

- It is equal to the voltage of the least significant bit(Vlsb) of the PCM code.

RESOLUTION

Resolution =Vmax

2n

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- The ratio of the largest possible magnitude to the smallest possible magnitude (other than 0V) that can be decoded by the digital-to-analog converter in the receiver.

DYNAMIC RANGE

DR = Vmax / Vmin

DR = 2n -1

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EXAMPLE

Determine the Dynamic range for a 10-bit sign-magnitude PCM code.

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EXAMPLE

For a resolution of 0.04V, determine the voltages for the following linear seven-bit sign magnitude PCM codes:

a) 0110101b) 0000011c) 1000001d) 0111111e) 1000000

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EXAMPLE

For the following resolutions, determine the range of the eight-bit-sign-magnitude PCM codes:

Code Resolution10111000 0.100111000 0.110011100 0.0500011100 0.0500110101 0.0211100000 0.0200000111 0.02

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EXAMPLE

Determine the minimum number of bits required for PCM codes with the following dynamic ranges and determine the coding efficiencies:

a. DR = 24 dBb. DR = 48 dBc. DR = 72 dB

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- A numerical indication of how efficiently a PCM code is utilized.

- The ratio of the minimum number of bits required to achieve a certain dynamic range to the actual number of PCM bits used.

==minmin

maxmax

X 100 %X 100 %

Where

minmin = min # of bits (including the sign bit)maxmax = actual # of bits (including the sign bit)

CODING EFFICIENCY

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EXAMPLE

Determine the number of bits required ina PCM code for a dynamic range of 80 dB. What is the coding efficiency?

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3. ENCODING

- The process of converting the quantized discrete-signal (PAM samples) to parallel PCM codes.

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FROM ANALOG SIGNAL TO PCM DIGITAL CODE

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SIGNAL-TO-QUANTIZATION NOISE

SQR(dB) = 10 log

Where:R = resistanceV = rms voltageq = quantization interval

V2/R

(q2/12)/R

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EXAMPLE

Determine SQR for a 2Vrms signal and a quantization interval of 0.2V.

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EXAMPLE

Determine the SQR for the following input signal and quantization noise magnitudes:

Vs Vn(V) 1 Vrms 0.01 2 Vrms 0.02 3 Vrms 0.01 4 Vrms 0.2

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LINEAR PCM CODES

- the magnitude change between any two successive steps is uniform

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FIGURE 11: LINEAR PCM CODES

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NON LINEAR PCM CODES

- the step size increases with the amplitude of the input signal

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FIGURE 12: NONLINEAR PCM CODES

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LINEAR VERSUS NON LINEAR PCM CODES

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MIDTREAD QUANTIZATION

- the first quantization interval is made larger in amplitude than the rest of the steps.

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MIDRISE QUANTIZATION

- the lowest-magnitude positive and negative have the same voltage range as all the other codes

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IDLE CHANNEL NOISE

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MASTERY EXERCISE

1. What are the different types of pulse modulation?2. What is the significance of the Nyquist Sampling rate?3. What type of modulation is effectively used by sampling

method?4. Describe the difference between natural and flat-top

sampling.5. Why is the used of a sample-and-hold circuit desirable?6. Define the process of quantization.7. What is quantization noise?

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MASTERY EXERCISE

8. What are the functional sections of a PCM modulator?9. What PCM functions does an analog-to-digital converter

perform?10. Why is a sample-and-hold circuit required in the PCM

decoder?

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SEATWORK

1. Determine the Nyquist sampling rate for the following maximum analog input frequencies:

a) 2kHzb) 5kHzc) 12kHzd) 20kHz

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SEATWORK

2. Determine the alias frequency for the following Nyquist sample rate:

fa(kHz) fs(kHz)

3 45 86 85 7

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SEATWORK

3. For the sample and hold circuit, determine the largest value of the capacitor that can be used for the following parameters: Z1 output impedance = 15ohms, an on resistance of Q1 of 15 ohms, an acquisition time of 12 microseconds, a maximum output current from Z1 of 10mA, an accuracy of 0.1%, and a maximum change in voltage in dv = 10V.

SIMPLEX PCM TRANSMISSION

BANDPASSFILTER

BANDPASSFILTER

SAMPLEAND

HOLD CIRCUIT

SAMPLEAND

HOLD CIRCUIT

ANALOG-TO-DIGITAL

CONVERTER

ANALOG-TO-DIGITAL

CONVERTER

PARALLEL-TO-SERIAL

CONVERTER

PARALLEL-TO-SERIAL

CONVERTER

SERIAL-TO-PARALLEL

CONVERTER

SERIAL-TO-PARALLEL

CONVERTER

DIGITAL-TO-ANALOG

CONVERTER

DIGITAL-TO-ANALOG

CONVERTER

HOLD CIRCUITHOLD CIRCUITLOWPASS

FILTERLOWPASS

FILTER

REGENERATIVEREPEATER

REGENERATIVEREPEATER

REGENERATIVEREPEATER

REGENERATIVEREPEATER

CONVERSIONCLOCK

LINE SPEEDCLOCK

SAMPLEPULSE

LINE SPEEDCLOCK

CONVERSIONCLOCK

SERIALPCM CODE

SERIALPCM CODE

PARALLEL DATA

ANALOGINPUT

SIGNAL

ANALOGOUTPUTSIGNAL

FIGURE 8: OUTPUT SPECTRUM OF SAMPLE AND HOLD CIRCUIT

AUDIO

fs 2fs 3fs

fs 2fs 3fs

frequency

frequency

fs - fa fs + fa

2fs + fa

2fs - fa 3fs - fa 3fs + fa

4fs - fa

0

fs - fa fs + fa

2fs - fa

2fs + fa

3fs - fa

3fs + fa

0

SHADED AREAS INDICATESPECTRAL FOLDOVER