# Questions regarding design problem

My instructor in electrical circuits has given me the following creative problem:

Construct a communication chain, that follows the drawing below:

The input is an AM signal, $$\V_{send}=V_1\cdot cos(2\pi f_1t)+V_2\cdot cos(2\pi f_2t)\$$

The chain consists of:

$$\V_{send}\$$ $$\\rightarrow\$$ An amplifier $$\\rightarrow\$$ Transmitter antenna $$\\rightarrow\$$ Transmission through air with distance $$\d\$$ $$\\rightarrow\$$ Receiving antenna $$\\rightarrow\$$ An amplifier $$\\rightarrow\$$ $$\V_{rec}\$$

Plot the frequency spectrum of $$\V_{rec}\$$.

Okay, for this I have some questions.

1. I plan to use the HA-8089 antenna as my transmission antenna, but can I also use it as my receiving antenna, or do I need another antenna for that?
2. Are the amplitudes and frequencies in $$\V_{send}\$$ (by those I mean $$\V_1\$$,$$\V_2\$$,$$\f_1\$$,$$\f_2\$$) dependent of what antenna or amplifier I use, or can I choose the values as I like?
3. When the signal travels through the air, it gets damped. To calculate the dampening I intend to use this formula: $$\F=20log(d)+20log(f)+32.44−Gtx−Grx\$$. Where $$\f\$$ is the frequency and $$\Gtx\$$, $$\Grx\$$ are the gains for the transmitting and receiving antenna. But what frequency should I use? $$\f_1\$$, $$\f_2\$$, or a combination of the two?
4. And lastly: When I have the amplifier gains, the antenna gains and the signal dampening, how do I then combine all that information to calculate the received signal, $$\V_{rec}\$$? Would it just be: $$\V_{rec}=(V_{send}\cdot G_{amp} \cdot G_{trans} -dampening) \cdot G_{rec} \cdot G_{amp}\$$?

I know that was a lot of questions, but I need some help now, cause I haven't been able to find an answer.

## 1 Answer

1) Antennae can both transmit and receive, so you can use another of the same type, in principle. Sometimes you want one to be directional and the other to be non-directional, so they are generally different; a broadcaster often wants to be heard from every direction, so would choose a different transmit antenna.

2) Yes they are constrained by the antenna and the frequency range is given in the datasheet. Limits on the amplitude are not given because they are determined by conductors heating and electrical breaktown but unless you're using vacuum tubes for the amplifiers you are unlikely to approach them.

HOWEVER both frequency and amplitude are tightly constrained by national and international laws. You must learn your local laws and choose frequencies within your antenna's range that you are permitted to use, and restrict amplitude to the permitted transmit power (AND ERP which is transmitted power * antenna gain)

3) You have used a very unusual way of expressing an AM waveform. Normally it is expressed as the PRODUCT of two sinewaves : a carrier frequency and a modulating frequency (which is the desired output signal). The frequency you would normally consider for loss is the carrier, which in your case is (f1 + f2) / 2.

Note that f1 and f2 are usually very close together; the modulating frequency (baseband signal) can be expressed as either (carrier - f1) or (f2 - carrier) or (f2 - f1) / 2. F1 and f2 are called the "sidebands" around the carrier. Your chosen frequencies in step 2 must both be within the same legal "channel" which may be only a few kHz wide.

4) You probably want to study the Friis equation