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Signals and Spectra Chap. 2
v(t)
1
–5 –4 –3 –2 –1 0 1 2 3 4 5 6
t
–1
Figure P2–2
(a) Find the expression for the instantaneous power and sketch this result as a function of time.
(b) Find the value of the average power.
★ 2–4 The voltage across a 50-Ω resistive load is the positive portion of a cosine wave. That is,
v(t) = e 10 cos v 0t, ƒt - nT 0 ƒ 6 T 0 /4
0, t elsewhere
where n is any integer.
(a) Sketch the voltage and current waveforms.
(b) Evaluate the DC values for the voltage and current.
(c) Find the RMS values for the voltage and current.
(d) Find the total average power dissipated in the load.
2–5 For Prob. 2–4, find the energy dissipated in the load during a 1-hr interval.
2–6 Determine whether each of the following signals is an energy signal or a power signal, and evaluate
the normalized energy or power, as appropriate:
(a) w(t) =ß(t/T 0 ).
(b) w(t) =ß(t/T 0 ) cos v 0 t.
(c) w(t) = cos 2 v 0 t.
2–7 An average-reading power meter is connected to the output circuit of a transmitter. The transmitter
output is fed into a 50-Ω resistive load, and the wattmeter reads 25 W.
(a) What is the power in dBm units?
(b) What is the power in dBk units?
(c) What is the value in dBmV units?
2–8 A cable company provides a 0 dBmV signal at 843 MHz via a 75-Ω coaxial cable to a cable
modem which is located in a residence. This modem uses this downstream signal to produce the
downloaded data signal for the Internet subscriber’s computer via an ethernet connection.
(The uplink signal that is sent by the modem is on 33.5 MHz.) What is the power of the 843 MHz
signal that is supplied to the modem if the modem acts as a 75-Ω resistive load to this downstream
signal?
2–9 Assume that a waveform with a known RMS value V rms is applied across a 1,000-Ω load. Derive
a formula that can be used to compute the dBm value from V rms .