3.20 Analog signal processing problems  (Page 3/6)

Power transmission

The network shown in the figure represents a simple power transmission system. The generator produces 60 Hz and is modeled by a simple Thévenin equivalent.The transmission line consists of a long length of copper wire and can be accurately described as a 50Ω resistor.

1. Determine the load current $R_{\text{L}}$ and the average power the generator must produce so that the load receives 1,000 watts of average power. Why does the generator need to generate more than 1,000 watts of average power to meet this requirement?
2. Suppose the load is changed to that shown in the second figure . Now how much power must the generator produce to meet the same power requirement?Why is it more than it had to produce to meet the requirement for the resistive load?
3. The load can be compensated to have a unity power factor (see exercise ) so that the voltage and current are in phase for maximum power efficiency. The compensation technique is to place a circuit in parallel to the load circuit. What element works and what is its value?
4. With this compensated circuit, how much power must the generator produce to deliver 1,000  average power to the load?

Simple power transmission system

Modified load circuit

Optimal power transmission

The following figure shows a general model for power transmission. The power generator is represented by a Thévinin equivalent and the load by a simple impedance.In most applications, the source components are fixed while there is some latitude in choosing the load.

1. Suppose we wanted the maximize "voltage transmission:" make the voltage across the load as large as possible.What choice of load impedance creates the largest load voltage? What is the largest load voltage?
2. If we wanted the maximum current to pass through the load, what would we choose the load impedance to be? What is this largest current?
3. What choice for the load impedance maximizes the average power dissipated in the load? What is most power the generator can deliver?

Big is beautiful

Sammy wants to choose speakers that produce very loud music. He has an amplifier and notices that the speaker terminals are labeled" $8\Omega$ source."

1. What does this mean in terms of the amplifier's equivalent circuit?
2. Any speaker Sammy attaches to the terminals can be well-modeled as a resistor. Choosing a speaker amounts to choosing the values for the resistor.What choice would maximize the voltage across the speakers?
3. Sammy decides that maximizing the power delivered to the speaker might be a better choice. What values for the speaker resistor should be chosen to maximize the power delivered to the speaker?

Sharing a channel

Two transmitter-receiver pairs want to share the same digital communications channel. The transmitter signalswill be added together by the channel. Receiver design is greatly simplified if first we remove the unwantedtransmission (as much as possible). Each transmitter signal has the form $$\forall t, 0\le t\le T\colon x_i(t)=A\sin (2\pi f_{i}t)$$ where the amplitude is either zero or $A$ and each transmitter uses its own frequency $f_i$ . Each frequency is harmonically related to the bitinterval duration $T$ , where the transmitter 1 uses the the frequency $\frac{1}{T}$ . The datarate is 10Mbps.

1. Draw a block diagram that expresses this communication scenario.
2. Find circuits that the receivers could employ to separate unwanted transmissions. Assume the receivedsignal is a voltage and the output is to be a voltage as well.
3. Find the second transmitter's frequency so that the receivers can suppress the unwanted transmission byat least a factor of ten.