SITUATION

A transducer whose internal impedance is 600 ohms resistive generates 0.1 volt rms at a frequency of 1000 Hz. It is desired to transmit this signal over a telephone cable whose length is 2.5 miles (recall, 1 neper = 0.115 dB). The characteristic impedance of the line, Z ₀, is 600 ohms, and its loss is 0.40 neper per mile. The phase shift is 0.1255 radians per mile. All parameters are measured at 1000 Hz. The input to the line is to be amplified by amplifier A so as to feed the line at a level of 0 dbm. The output of the line is to be amplified by amplifier B so as to provide 2.0 watts to a recorder. Amplifiers A and B each have an input impedance of 600 ohms.

REQUIRED

1. What is the gain of amplifier A in decibels?

2. What is the gain of amplifier B in decibels?

3. What is the delay in microseconds between the input and output of the line?

4. What would be the least expensive way to reduce the 1000 Hz loss in the telephone line?

5. What effect, if any, would this measure in (d) above have on the line's delay?

   

SOLUTION

1. 
   

2. Loss in cable: 0.4 nepers/mile 2.5 miles = 1 neper

   1 neper 8.686 db / nepers = 8.686 db

   P _in = 0 - 8.686 = -8.686 dbm

   
   

3. Delay microseconds. ANS.

4. The loss at 1000 Hz could be reduced...