Hannah's+AM+Radio+Lab

= AM Radio Lab = March 3, 2010 media type="youtube" key="z_trSIBCgF0" height="344" width="425"
 * Participants**: Hannah Mollmark
 * Purpose**: The purpose of this lab is to learn about the different elements of a circuit (i.e. capacitors, inductors, diodes, etc) and how they interact and amplify an AC signal. In order to study this further, we learned how to build an AM radio, calculating the different parts to get the resonant frequency that will pick up a specific AM radio station. After having put together the radio, we figured out what needed to be altered and how, in order to get the desired resonant frequency and therefore the desired radio station.

capacitance = constant x area (m sq) / distance (m) C = ε  0 x A / d || inductance = ( constant x coils (sq) x area (m sq) ) / length (m) L = ( μ0 x N^2 x A ) / l || resonant frequency = (1 / 2 pi) x (1 / square root(inductance x capacitance) ) fres = (1 / 2 π ) x ( 1 / sqrt(LC) ) || The coefficient of static friction was determined to be 0.45. This was calculated from a measured angle using Newton's first law as desribed in the calculations.
 * Brief Description of Experiment**: In this experiment, we did early tests to become acquainted with the elements of a circuit including capacitors, inductors, resistors, etc. We also did online simlations to clarify these connections. After learning about the mathematical correlation between inductance and capacitance we were able to calculate values for both of these in order to create a a circuit with a specific resonant frequency (900K Hz). After many trials and tribulations, we finally figured out that the capacitor would need an area of .04 m sq and a distance between the two sheets to be 6.7 x 10^-5 (which is about the thickness of a piece of paper) to create a capacitance of 5.28 x 10^-9. The inductor needed five coils of wire with a length of about .015m to create an inductance of 1.3 x 10^-5. This created an LC of 6.864 x 10^-14 which was very close to the target LC of 3.13 x 10^-14. When we put together our radio and attached it to ground and an antenna, we listened for a station and then altered the distance of the capacitor to see if we could either strengthen or change the station.
 * Sample Calculations:**
 * //Capacitor calculation// || The capacitance in farads is calculated by mulitplying the constant by the area of the capacitor divided by the distance between the two parts (pieces of foil) of the capacitor.
 * //Inductor calculation// || The inductance in henries is calculated by multiplying the constant by the number of coils squared and the area of the coils and then divided by the length of the coils.
 * //Resonant frequency// || The resonant frequency is calculated by mutiplying one divided by two pi by one divided by the square root of the capacitance mulitplied by the inductance.
 * Results**: Describe the major result of the experiment and how you arrived at this result. Typically, this will refer back to the purpose. For example, if the purpose was to find the coefficient of friction, you would write:

//Explain what a resonant circuit is, what circuit elements it contains, and how those elements work together to amplify an AC signal.// A resonant circuit consists of a capacitor and inductor and alternates at the resonant frequency which is the frequency that works best and is most efficient for both the inductor and capacitor at the same time. A resonant circuit has a repeating movement that is created when the inductor creates a current that, in turn, charges the capacitor, and then as the capacitor discharges, it makes a current that charges the inductor. This creates a back and forth motion that keeps the circuit running. The resonant frequency is what allows this to function at its highest capacity and efficiency. In order to amplify an AC signal, the elements have to work together in this way, charging, discharging, and recharging in a cycle. The parts of the circuit need to be accurately built in order for the calculations to be accurate and the right resonance frequency to be reached. There are a lot of little elements that need to be "perfect" for the entire system to work efficiently and accurately.
 * Lab Questions**:

//Describe (pictures, calculations, etc) your particular resonant circuit and its elements. What is its resonant frequency and how do you know?// According to our calculations, we determined that the capacitor would consist of two sheets of aluminum foil that were 0.2m x 0.2m (20cm x 20cm) and one sheet of paper apart which is a distance of about 6.7 x 10^-9 m. To make our inductor, we coiled wire around a water bottle with a diameter of 0.09m (9cm) five times. We estimated it's length (coiled) to be about 0.015m (1.5 cm) and it's area to be 0.00636m. We set up these two with a diode, headphones, and antenna and ground sources. Using the resonant frequency equation (displayed in the calculations chart above), our resonant frequency is 607,479Hz or 607kHz. I know this because we started by separating LC from the resosnant frequency equation: 1 / 2pi = 0.159 0.159 x (1 / sqrt(LC)) = 900000 0.159 = 900000 x (sq rt(LC)) 1.77 x 10^-7 = sq rt (LC) LC = 3.12 x 10^-14 Capacitor (five coils around a water bottle with diameter of 9cm); Inductor (20cm x 20cm foil one page apart); Headphone

//Address one of the following (more for EC): effect of resistance on resonance; diodes and demodulation; head phones and electric to audio conversion; antennas and conversion of AM waves to currents. Diodes and Demodulation: A diode is a "two-terminal electrical component" (1) through which electric current can only flow one direction. Diodes are used to change alternating current into direct current as well as demodulating from radio signals in radio receivers. The initial purpose for the diode was to demodulate amplitude modulated, or AM, radio. This works in that AM signals are made up of positive and negative voltages; it's amplitude (also known as envelope) is proportional to the original audio signal. The diode rectifies, or changes alternating current to direct current, and blocks the positive or negative parts of the waves, thus resulting in the original audio signal without atmospheric noise. When the signal is then put through a filter and audio amplifier, sound waves are created. // (1) http://en.wikipedia.org/wiki/Diode


 * Conclusion**: I believe that our AM radio experiment produced a valid and reproducible result because we constructed our radio based on calculations and measurements of the devices that we created ourselves. Also, we used a design circuit given to us so it is reproducible; we, in fact, rebuilt our radio multiple times from day to day. Our results might differ from accepted or expected results because as we discovered, our radio usually worked (better) when the capacitor was taken out of the circuit. We discovered that this could be because the antenna acutally has its own capacitance which was enough to work in our circuit because we had designed our radio for a very small capacitance. A simple improvement that could be made to our radio would be to design it for a greater capacitance so that it would not be influenced by capacitances "accidentally" created.

//Don't forget to link to your lab report from the lab reports page and to include a link to your lab report in your reflection.//