# Communications Systems Hw 1 Week 1

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ECET 310
Week 1 – Homework 1_1

(a) 60 dB + 25 dB = 85dB (b) 20 dBW + 5 dBW = 25dBW

(c) 22 dB - 4 dB = 18dB

2. Convert:

(d) 65 W into dB 10 log 65 = 18.1 Db

(e) 10 dB into watts 10/10 = log x => 10W

(f) – 5 dB into watts -5 = 10 log x x=10 ^(-5/10) = 0.316 (g) –30 dBm into dBrn 30 dBrun (h) 15 dBrn into dBm 10 log (p/1mW)
15/10= log (p/1mW)
1.5 =log (p/mW) = -15dB

AP3 = 30
AP2 = 25
AP1 = 10

2. A three-stage amplifier is shown with power gains. Calculate total power gain in decibels, and as a number.

Ap(tot) = (Ap1)(Ap2)(Ap3) = 7500
Ap(tot) (dB) = 10 log(10) +10 log (25) +10 log(30) = 38.75dB

AP3 = 20
AP2 = 10
AP1 = 10

3.

(a) Determine the overall power gain. (b) Find the output power if Pin = 15 mW

a) Ap(t) = (10)(10)(20) = 2000 b) Po = (Pin)(Ap(t)) = (15mW)(2000) = 30W

AP3 = -6 dB
AP2 = 16 dB
AP1 = 13 dB

4. If Pin = -20 dBm, determine the output power in dBm and watts.

Ap(t) = 13+16-6 = 23dB
Ap(t) = log^-1 (23/10) = 199.526
Pin = -20dBm = (1mW)(log^-1(-20/10)) = 1mW* 10^-2 = 10 uW
Po = (Pin)(Ap(t)) = 10u*199.526 = 1.995 mW
Po(dBm) = 10 log (Po)/1mW = 10 log (1.995mW/1mW) = - 27dBm

PS = 0.1W

AP1
AP2

AP1 = 400 L = 2000 AP2 = 500
RL
0
1

5. Determine:

(a) Net gain (b) Net gain in dBs (c) Power output

a) Ap(t) = (Ap1)(1/L)(Ap2) = 400*(1/2000)*500 = 100

b) Ap(t)(dB)= 10 log (100) = 20dB

c) Po = (Pin)(Ap(t)) = 0.1W*100 = 10W

PS = -8 dBm

AP1
AP2

AP2 = 28 dB AP1 = 32 dB L = 24 dB
RL
0
1

6. Determine:

(a) Net gain (b) Net gain in dBs (c) Power output

a) Ap(t) = Ap1 –L +Ap2 = 32dB-24dB+28dB = 36dB
Ap(t) =...

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