chapter 2 - sonoma state university• leon w. couch ii, digital and analog communication systems,...
TRANSCRIPT
![Page 1: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/1.jpg)
Chapter 2
Signals and Spectra Updated:2/2/15
![Page 2: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/2.jpg)
Waveform Properties • In communications, the received waveform r(t) basically
comprises two parts: – Desired signal or Information – Undesired signal or Noise
• Waveforms belong to many different categories – Physically realizable or non-physically realizable – Deterministic or stochastic – Analog or digital – Power or energy – Periodic or non-periodic
r(t)
![Page 3: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/3.jpg)
Waveform Characteristics (Definitions)
Wdc = w(t) = w(t)Note:
p(t) =
av
norm
Pnorm =Pav, when RLoad=1
w2 (t) =WrmsNote:
Note : w(t) can be v(t) or i(t)
If w(t) is periodic with To, lim1/Tà1/To
Pav = p(t) = v(t) ⋅ i(t)
Note that [ . ] is the function! < > is the operation!
w(t) can related to v(t) or i(t) Note that in this expression [ . ] is w(t)!
Different expressions
![Page 4: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/4.jpg)
Waveform Characteristics (Definitions) Remember: < > is the time average operation! Average power is average of instantaneous power!
Note that rms is derived from time average ( <[.]2> )1/2
Average Power At the load: Pav V(t) across the load; with i(t) going through the load
Pay attention: <[.]2> is different from <[.]>2
![Page 5: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/5.jpg)
Real Meaning of RMS
RMS for a set of n components
RMS for continuous function from T1 to T2
RMS for a function over all the times
![Page 6: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/6.jpg)
Waveform Characteristics (Summary)
See Notes:2a
Wdc = w(t) = w(t)Note:
p(t) =
av
norm
Pnorm =Pav, when RLoad=1
w2 (t) =WrmsNote:
Note : w(t) can be v(t) or i(t)
If w(t) is periodic with To, lim1/Tà1/To
Pav = p(t) = v(t) ⋅ i(t)
![Page 7: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/7.jpg)
Energy & Power Waveforms
Energy_ Signal→ 0 < E <∞Power _ Signal→ 0 < P <∞
Signal Definition:
Note that a signal can either have Finite total normalized energy or Finite average normalized power
Note: If w(t) is periodic with To, lim1/Tà1/To
Remember:
*
*
![Page 8: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/8.jpg)
Example
Periodic Signal!
Voltage
![Page 9: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/9.jpg)
Example (continued)
* Instantaneous Power:
Voltage
Current
Average Power
Pav = p(t) = v(t) ⋅ i(t)Note:
(it is a function of time!)
Pav =Vrms ⋅ Irms
V = Vpeak
![Page 10: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/10.jpg)
Example (continued)
* Instantaneous Power:
Voltage
Current
Average Power
Vrms = v2 (t) =1T0
[V cos(wot)]2 dt
−To/2
To/2
∫
Vrms =V2; Irms =
I2;
Pav =Vrms ⋅ Irms =V ⋅ I2
Note that this is only true when V(t) is a sinusoidal. In this case V is the Peak amplitude of v(t)
`
V = Vpeak
Incandescent light bulbs flicker at twice the AC frequency, because the filament grows a bit hotter each time the current peaks. So: 50 Hz AC => 100 Hz flicker;
![Page 11: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/11.jpg)
RMS Values
http://en.wikipedia.org/wiki/Root_mean_square
![Page 12: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/12.jpg)
Example – Using the Scope Note that RMS is Vpeak/SQRT(2)
Signal: Freq=5MHz, Vp=250mV; offset=0mV
Find Period, RMS, Average (DC), & Vpp!
![Page 13: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/13.jpg)
Example – Using the Scope Note that RMS is Vpeak/SQRT(2)
Signal: Freq=5MHz, Vp=250mV; offset=0mV
Note: RMS=250/sqrt(2) = 176mV; Average (DC) = 0mV
![Page 14: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/14.jpg)
Example - Scope Note that RMS changes as the waveform Changes; independent of the frequency
Note: RMS=250 mV; Average (DC) = 0mV
![Page 15: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/15.jpg)
Example - Scope Two signals being multiplied by each other! Vmul = [V cos(wot)]
2 =V 2
2(1+ cos(2wot)]
Offset= V2/2
Slightly out of phase!
![Page 16: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/16.jpg)
Example - Matlab
Assume v(t) and i(t) are in phase. Plot the p(t).
![Page 17: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/17.jpg)
Example • v(t)= et is a periodic voltage signal over time interval 0<t<1.
Find DC & RMS values of the waveform
![Page 18: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/18.jpg)
Example • v(t)= et is a periodic voltage signal over time interval 0<t<1.
Find DC & RMS values of the waveform
![Page 19: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/19.jpg)
Decibel
System Pin Pout Power and dB expression:
Remember: Pav = V2rms/R
Remember: Pav = I2rms x R
If power ratio is positive à GAIN If power ratio is negative à ATTEN If power ratio is zero à Unity GAIN
![Page 20: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/20.jpg)
Signal-to-Noise Ratio System
S N
System S N
OR
To load
![Page 21: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/21.jpg)
dB vs dBm
http://www.rapidtables.com/electric/dBW.htm
![Page 22: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/22.jpg)
dBW vs dB
![Page 23: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/23.jpg)
dBm vs dBW
![Page 24: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/24.jpg)
Example
Vrms=1.78V V(t) = e^t
(at t=0) System S Load
![Page 25: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/25.jpg)
Phasor Complex Number
(y/x)
Note that when we use Phasor representation the frequency information is ignored!
Remember: Complex numbers can be expressed using Cartesian or Polar Coordinate Systems
![Page 26: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/26.jpg)
More on dB…. • Read on your own
![Page 27: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/27.jpg)
![Page 28: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/28.jpg)
![Page 29: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/29.jpg)
![Page 30: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/30.jpg)
You Should Know… • Time Average • Dc Value • Power • Instantaneous Power • Average Power • RMS • Normalized Power • Energy And Power Waveforms • Decibel • dBm And dB And dBW • Signal-to-noise Ratio • Phasor Representation
![Page 31: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/31.jpg)
DEMO
![Page 32: Chapter 2 - Sonoma State University• Leon W. Couch II, Digital and Analog Communication Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System:](https://reader030.vdocuments.site/reader030/viewer/2022040114/5e2b9235e715b60f857d1b42/html5/thumbnails/32.jpg)
References • Leon W. Couch II, Digital and Analog Communication
Systems, 8th edition, Pearson / Prentice, Chapter 1 • Electronic Communications System: Fundamentals Through
Advanced, Fifth Edition by Wayne Tomasi – Chapter 2 (https://www.goodreads.com/book/show/209442.Electronic_Communications_System)