Analog Electronics AGH Class Exercises

Data transmission

Exercise 1 Connection

A signal is digitalized with rapidity 1200 bauds and number of symbols m=4. This signal is transmitted in NRZ format by a cable of bandwidth B_cable =0-3.4kHz

What is the bit rate and bandwidth B_signal of emitted signal?

Is it possible to increase the bit rate using the same cable, if yes how ?

Exercise 2 RS232 connection

The serial communication type RS 232 is one of the oldest digital connections commonly used to connect PCs with the GPS, mustimeters, modems etc. Presently is replaced by serial connection USB, internet and by radio connections (Bluetooth, WIFI).

1. Give and illustrate the structure of a RS 232 character. How many bits is it possible to transmit using RS 232, what is the dynamic of numeric signal, how many symbols can transmit RS 232

2. The RS 232 is it synchrony or asynchrony system?

3. How does a receiver detect the character start ?

4. Suggest the block diagram of C 232 receiver

5. One character is coded using 8 bits. Rapidity of transmission is 6 kbauds. What is the bit rate?. What is the bandwidth B_sig of emitted signal. What is the maximal cable length L for this connection (ref Tab. below)

Exercise 3 Conversion A/N and synchrony transmission of an audio signal

The audio stereo signal is digitized in order to record it on the CD disc.

The digitizing parameters are as follows:

• Dynamic – 96 dB

• Bandwidth of analog signal 0-15 kHz

Suggest :

• Minimum sampling frequency

• Bit resolution and equivalent number of symbols

• What is the equivalent bit rate of this signal

• This signal is transmitted by a cable type “twisted pair “ using Manchester code. What is the bandwidth of this signal

• Attenuation of such a cable is given by formula :

α(f)=Kf² (1)

where :

− α is attenuation coefficient in dB/km,

- f is frequency in MHz

- K=1 dB/km/MHz²

Such a cable acts like a low pass filter and its cut off frequency is given as

$f_{c} = \sqrt{\frac{3}{\text{KL}}}$ (MHz) (2)

What will be maximal length Lmax if the synchrony connection is used?

Exercise 4 Error probability in synchrony transmission

The data transmission system emits the NRZ type signal with the bit rate 10⁴ bits/s. The pulse amplitude measured at the receiver input : A = 10mV.

-the received signal is embedded in background noise of spectral density N_o= 410^-11 W/Hz.

-the cable used is adapted to emitter and receiver;

-the input receiver and output emitter resistivity’s are R=50Ω.

- the systems fulfils the requirements of synchrony transmission B_cable = B_rec =B_signal/2 .

1. What should be characteristic resistivity of cable

2. Give the bandwidth of emitted signal and its bit rate

3. Give the background level power N at the receiver input

4. Give the received signal power P_r (i.e of one bit bit)

5. Give the signal to noise ratio SNR , lin. and dB

e. Error probability P_err , for NRZ signal is given by formula shown in figure where Estimer P _err.

f. The bit rate is increased 10 times. How should be modified amplitude A in order to keep same P_err

g. The cable length is L=100 km ;

- estimate the cable attenuation α(f) (take f=f_max=B_cable) use the graph from exercise 3

- give the required power P_edBm and P_e at the emitter output; (take the parameters as in case (f) ).