Communication Systemsweek 2

Tech 163

Issues or concerns? Questions?

Homework

For amplitude = 1, terms are: 4/π + 4/3π + 4/5π …

1.2

1.4 Convert to deg K 273 + 27 = 300 deg KNoise Power = kTB where k = Boltzmann's const =1.38 x 10 ^-23 and B = noise bandwidth = 10 k HzSol = 1.38 * 300 * 10^-23 * 10*10^3

= 4.14 * 10^-17 W

1.8 (S + N)/N = 5/.2 = 25In dB this is 10 log 25 = 10 * log 25 = 10 * 1.39 = 13.9 or rounded to 14 dB

Homework (continued)

1.9

1.12 Power gain = a1 * a2* a3 = 10*25*30 = 7500NF = NF1 + (NF2-1)/a1 + (NF3-1)/ a1*a2 = 2 + (3/10) + (4 / (10*25)= 2.316

31 s/n = 30 dB in and 27.3 dB out what is NF? NF in dB is subtraction, 30 – 27.3 = 2.7 dB NF ratio = anti log (2.7 / 10 ) = 1.86Tn = 290*(NF-1) = 290*.86 = 249.4 K

NF = (S/Nin) / (S/N out) = 100 µ/1µ / 1/.03 NF = 100/33.33 = 3.0

Homework (continued)

32

33 Tn = 290 (NF-1) 100 = 290 *(NF -1) NF – 1 = 100/290 = .3448 NF = .3448 + 1 = 1.345 or 1.29 dB

Second receiver has a better NF = 1.31 Therefore: it degrades the input less than the 100 K receiver. So all things being equal, the second receiver is better.

Time for Quiz 1

S/N = 100µ/2µ =50 convert to dB = 20 log 50 = 20*1.69in = 33.98Output dB = 30 NF = 33.98– 30 = 3.98dB = anti log (3.98/20) = 1.58Note use of the voltage dB formula.

Chapter 2

Once frequency gets into the range that would support radiation, circuit elements change their appearance and become more reactive.

Since we use these components in telecommunications to trigger high frequency oscillations, we may find we get these oscillations in places we don’t want them. Terms used:

Carrier = high frequency signal that will radiatebaseband = low frequency signal containing informationbandwidth = frequency range needed to support

communication of informationOne thing that the text is attempting to point out is that circuits that radiate were difficult to obtain. Early inventors could only achieve the frequency necessary by creating arcs. In this chapter we study oscillators that can reach the high frequencies necessary for modern transmission.

Oscillators

In order to oscillate, the charges (electrons) in a circuit must experience a force that moves them in a repeating manner. To do this, the force must be just the right amount, too much and the circuit overloads, too little and the oscillations die out.Technically this means that the

loop gain must be just enough to cover any dampingthe phase of the feedback must be right to add to the signal

(compensation for the damping)

So oscillation depends on the damping in the circuit.

Note that oscillation is driven at the circuit’s resonant frequency to make it easy to sustain oscillations.

Experiment

This experiment is about Phase

Do you see how phase plays into keeping an oscillator going?

In this case force was input to the spring, so it was negative

If the force were directed toward the mass (golf ball), what direction would it be?

Can the force be put in either direction?

What does positive feedback mean?

Hartley Tank Circuit

Resonant Frequency

http://www.electronics-tutorials.ws/oscillator/hartley.html

A resonant circuit produces harmonic oscillations. (like a suspended mass on a spring for example this is the formula for the resonance of a Hartley Oscillator)

Hartley Circuit

Example calculationLet Lt = 1 mH and let C = 100 pF

1 * 10^-3 * 100 * 10^-121* 10^-1310 *10^-14

Colpitts Tank

http://www.electronics-tutorials.ws/oscillator/colpitts.html

Basic Colpitts

Math ProblemStudents start a painting business in the summer

A can paint a Condo in 2 hoursB can paint the same Condo in 4 hoursC can paint the same Condo in 5 hours

If they do not interfere with one another, how long does it take to paint the Condo if they work together?

This applies to series and parallel circuits

Series rule Inductors and resistors add, Capacitors use reciprocal ruleInductor Resistor Capacitor

. + =.

Parallel rule Capacitors add, Inductors and Resistors use reciprocal rule

+ = + =

Frequency Colpitts

Practical Oscillator Circuits

OK, we have oscillations, and we can substitute crystal oscillators for part of the resonate circuit, (we gain stability, accuracy, and reduce size)

Now we want frequency selection.

Voltage Controlled OscillatorsCrystal Controlled OscillatorsMixer frequenciesFrequency Synthesizers

VCOA voltage-controlled oscillator or VCO is an electronic oscillator whose oscillation frequency is controlled by a voltage input. The applied input voltage determines the instantaneous oscillation frequency.Source: https://en.wikipedia.org/wiki/Voltage-controlled_oscillatorHere is a circuit oscillator controlled by a voltage input: source: http://www.radio-electronics.com/info/rf-technology-design/pll-synthesizers/vco-voltage-controlled-oscillators.php

Colpitts or Hartley?

VCO Theory

http://slideplayer.com/slide/236711/

Crystal

Here is a Colpitts circuit augmented with a crystal Source google.com The crystal is used in the place of the inductor

Mixer

A mixer circuit will produce both sum and difference frequenciesSource: http://michaelgellis.tripod.com/mixersin.html

Phase Locked LoopsFrequency Synthesizers

We are looking for frequency agility, the ability to quickly change frequencies. Where would this be useful?A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. While there are several differing types, it is easy to initially visualize as an electronic circuit consisting of a variable frequency oscillator and a phase detector. https://en.wikipedia.org/?title=Phase-locked_loopSource: http://www.radio-electronics.com/info/rf-technology-design/pll-synthesizers/phase-locked-loop-tutorial.php

Advanced PLL

This system has the advantage of being able to set a divider to provide for incremental adjustment of the loop frequency. For example, the frequency can be adjusted in 10 MHz steps, displayed on a control panel… https://en.wikipedia.org/?title=Phase-locked_loop

Engineering Problem

• A transmitter frequency is loaded via a hard line network. The sequence is:– Verify system is OK-- locked on start up frequency– Send new frequency– Verify system is OK --locked on new frequency– If not OK, stop otherwise proceed

• Problem: While changing the frequency synthesizer the system check is set to fail, depending on the time required to change frequencies, the result is a possible failure of the system. What is a possible solution for this problem?

Solution

• Three solutions were proposed– Calculate the worst case timing and see if the fail would

actually occur (Result = 4 ms margin --Risky)– Add a wait state to delay the second check (Resulted in huge

cost penalty)– Modify system so that after an OK result the system check

was left in the OK state during subsequent frequency changes (Small cost, but could not catch initial system)

– Final solution, accept risky approach with small margin for initial system run, & change the system to leave status in the OK state for frequency changes for subsequent system builds.

Assignment

• Read Chapter 2; skim details about amplifier class and oscillator design, (come back to this next week)

• Show example 2.4 solved• Show example 2.7 solved• 1. A resistor is wire wound, what happens when

this device is used in a high frequency circuit?• Problem 29,33