Am+Radio+Lab

=AM Radio Lab= 3/3/10
 * Participants**: Trevor Wood
 * Purpose**: The purpose of this lab is to create a radio that picks up a certain AM signal by creating a resonant circuit that amplifies the carrier frequency.


 * Brief Description of Experiment**: In this experiment we needed to create a Radio using an antenna as the battery source, a capacitor and inductor as the resonator, a diode as the demodulator, a head phone as the electric audio, and a ground. A diagram of this can be seen below. This radio contains a resonant circuit or LC circuit, which is an inductor (L) and capacitor (C) which creates a current that oscilates allowing you to find the resonant frequency. The resonant frequency that we were attempting to make was 900K Hz. In order to find this we plugged 900 as the resonant frequency in the formula. After rearranging the formula we found that LC equaled 3.1279703 x 10^(-14). The next step was solving for either the variable L or C. We decided to start with the inductor and plugged in 50 for the number of coils in the wire each with an area of 0.028m that stretch out over a length of 0.08m. This gave us the value of .001 Henries for the inductor. With the inductance we were able to find the capacitance which equaled 2.80934884 x 10^(-11) we divided this by the constant and were able to find the value of A / d. We then decided to make the area of the foil 0.12697m^2 and the only variable left to find was the distance which ended up being 0.04m. With all the values for the variables we created a radio and connected it to the antenna and ground. At first we did not get any signal but by adjusting the capacitance we were able to pick up a signal of what we think is 1400AM, not our target 900AM.


 * 1.Diagram of Radio (**top left)
 * 2. Radio Picture** (top right)
 * 3. Capacitor** (bottom left)
 * 4. Inductor** (bottom right)



In order to pick up the target station of 900AM we needed to create a resonant circuit that would amplify the carrier frequency. To do this we created an inductor and capacitor, which together act as a resonator in our radio. The resonator along with an AC source, that was set to equal the resonant frequency, we aplified the carrier wave making the current larger and allowing us to pick up a stronger AC signal.


 * Above:** The top wave is a sound wave. The middle wave is a carrier wave which has a high freq. The bottom wave is an AM signal, that gets picked up by an antenna in a radio.

The way are radio was able to produce sound started with the original sound wave that is sent out from a radio tower. These waves are then multiplied with carrier waves, which produce an amplitude modulated signal (AM signal). This AM signal is then picked up by our antenna. Now once it has entered the radio it goes through the resonator (inductor and capacitor) which selected the specific frequency from the signal for the radio station that we wanted. Then this wave is pushed though the diode which acts as a demodulater creating a one way valve for current. THis essentially only lets the positive part of the wave to pass and discards the negative part, this gives you a sound wave. THis sound wave is then finally sent to the headphone where the radio can actually be heard.

math \frac{1}{2\pi \sqrt{LC}} math || C = ε 0  x ( A / d) ε 0 = 8.85 x 10^(-12)  || L = ( μ 0  x (N^2) x A ) / l μ 0 =4π x 10^(-7) ||
 * Sample Calculations:**
 * //Resonant Frequency Formula// || The Resonant Frequency is found by multiplying (1/2pi) by (1/(inductor(H) x compacitor(F))^.5)
 * //Capacitor Formula// || The capacitance(Farads) is found by dividing the area of the sheets of foil by the distance they(the two sheets of foil) are from each other and multiplying that answer by ε 0 .
 * //Inductor Formula// || The inductance(Henries) is found by multiplying the constant μ 0 by the number of coils in the wire raised to the second power and by the area of one of the coils in the wire. This answer is then divided by the length of all the coils of the wire.


 * Conclusion**: Our radio turned out working proficiently after some minor adjustments the the capacitor. At first the sound was very faint, but eventually we made enough adjustments to the point were we could here the words perfectly from the radio, although at somewhat of a low volume. Since making the radio was a very complex process with many oppertunities of error there could have possibly been some parts, either during the calculations or during the construction of the radio, that were incorrect. This could explain why we picked up the station 1400AM instead of our target 900AM. Perhaps when calculating the resonant frequency we made an error causing it to be higher then 900K Hz like we had wanted. Another error was that our capacitor was built alittle wrong. The two foil sheets were placed at a farther distance then they should have. After fixing this problem the sound was much clearer and louder. Another aspect of the radio that caused some minor problems in the amplitude of the sound was the antenna, which was moved from place to place through out the experiment. ALthough we got sound at each of the antenna locations, some produced better sound then others because of how the different set ups of the antenna pick up either better or worse radio signals.