ELEC 241 Lab

Design

Looking at the diagram of our system in Figure 9.2 we already have some of the components that we need: The mixer amplifier from Experiment 4.3 will convert the acoustic source signal to an electrical signal, and the earphone amplifier from Experiment 6.2 will convert the received electrical signal back to an acoustic signal. That leaves just the transmitter, antennas (to interface to the wireless channel) and the receiver.

Part A: The Transmitter

The function of the transmitter is defined by the equation
$$x(t)=A_c\bigl(1+m(t)\bigr)\cdot\cos(2\pi f_ct)$$
If we dissect this equation, we can identify the following five things we need to do
  1. Generate the source signal \(m(t)\). (We've already done this with the microphone and mixer amplifier.)
  2. Add one. (We can do this with an op-amp.)
  3. Generate the carrier signal \(\cos(2\pi f_ct)\). (We can do this with the function generator.)
  4. Multiply the carrier signal by \(1+m(t)\). (We don't know how to do this with an op-amp.)
  5. Multiply by \(A_c\). (Depending on \(f_c\) and \(A_c\) we may or may not be able to do this with an op amp.)
Unfortunately, the one thing we can't do with an op-amp (step 4) is the core of the modulation process. In fact, multiplying two signals is challenging regardless of the circuit components we have available. Fortunately, multiplying two numbers is a trivial operation for a computer, so if we're willing to use the computer as part of our system, we can proceed.

Part B: Choice of Carrier Frequency

Since the maximum sampling rate of our D/A converter is \(f_s=1.25~\text{MHz}\), the maximum carrier frequency we can use is \(f_s/2=625~\text{kHz}\). If we consult Part 15 of the FCC regulations, we find the only frequencies in this range where we can legally transmit significant amounts of power are in the \(160-190~\text{kHz}\) band.

Part C: Antennas

The down side of using frequencies in the \(160-190~\text{kHz}\) band is that the wavelengths are long (greater than \(1.5~\text{km}\)). Since an efficient antenna has to be on the order of the wavelength, we are restricted to using antennas which are very inefficient. For a simple antenna we have two choices: an electric antenna, which is basically a long piece of wire (like the radio antenna on your car) or a magnetic antenna, which is simply a coil of wire. Since we can increase the effective size of a magnetic antenna without increasing the physical size by adding additional turns to the coil, we will choose a magnetic antenna.

The antenna we will use consists of 8 turns of wire in a loop of diameter 65 cm.

Part D: The Receiver

The optimum (coherent) AM receiver is shown in Figure 9.4 in the previous section. The core of this receiver is nearly identical to that of the transmitter: the received signal is multiplied by a sinusoid at the carrier frequency. In addition, the received signal is bandpass filtered to reduce noise and the demodulated signal is lowpass filtered to eliminate the copy centered at \(2f_c\).

As with the transmitter, we will have to use the computer to multiply the received signal by the carrier. Since we can build much better filters digitally than we can with analog circuits, we'll do the filtering portion of our receiver in Labview as well.

Here's the list of required receiver functions:

  1. Bandpass filter \(r(t)\) to produce \(\tilde{r}(t)\).
  2. Generate the carrier signal \(\cos(2\pi f_ct)\).
  3. Compute \(\tilde{r}(t)\cos(2\pi f_ct)\).
  4. Lowpass filter to produce \(\widehat{m}(t)\).

Part E: Antenna Interface Module

We've completed most of the hard part of the design, at least in terms of signal processing, now all we need to do is connect them all together. Here's a list of the remaining tasks:
  1. Connect the transmitter and receiver to the antenna.
  2. Since the transmitter and receiver share a single antenna, we need a way to switch between them.
  3. Because of the low efficiency of the transmitter antenna, we need a large amount of electrical power to produce a radiated EM wave of usable strength. I.e. the transmitter requires an amplifier with high power gain.
  4. Similarly, the low efficiency of the receiver antenna means that even a strong EM wave will produce a small electrical signal. We should also amplify the received signal before processing it.
  5. To improve the effective efficiency of the antenna, we should match its impedance to that of the amplifiers.
  6. Since we will be using DSP for our signal processing, we should lowpass filter the received signal to prevent aliasing and the transmitted signal to remove harmonics.

Given that there are only four more weeks in the semester and that we need to learn Labview before we can do the hard part, it might be a good idea to outsource this last Part of the design. Fortunately, there's an empty spot on the breadboard where we can install an additional Interface Module.

The circuit below provides the necessary functions:

Click to enlarge.

Here's how it works:

Here's what it looks like:

Make sure that the antenna module is installed on your breadboard when you're ready to use it. Talk to your labbies or Mr. Randy Fly if you don't already have one on your board. The connection for the transmitter is on pin 39 of the interface connector and the connection for the receiver is on pin 29.