UNIVERSITY OF CALIFORNIA, BERKELEY EE40 Fall 2009 Lab 1 Introduction to Circuits and Instruments Guide 1. Objectives The electronic circuit is the basis for all branches of electrical engineering. In this lab, basic electronic circuit theory, electronic and photonic devices will be introduced and employed. Fundamental testing equipment will be used to measure and characterize simple circuitry. In the hands-on lab, you will apply these basic theories to the devices and components provided to design simple circuits. 2. Basic circuit theory and devices In this section, some basic circuit theory will be presented first. You will need to apply this to the following hands-on lab to design your circuit. Simple electronic and photonic devices such as resistors, light emitting diodes (LEDs) and speakers/microphones will also be discussed and used in the lab. Before doing the lab, please read through this section carefully and complete the prelab to test your understanding of the material presented here. (1) Ohm’s Law: V = IR Current (denoted I) and voltage (denoted V) are two major quantities that are used to study electronic circuits. Current is the amount of charge passing through a certain area in a unit time period, while voltage describes the electrical potential drop across any two nodes in a given circuit. Ohm’s Law states that the voltage V across an ideal resistor is proportional to the current I through the resistor. The constant of proportionality is the resistance R of the resistor. I V + R V Slope = R - I V ! IR Figure 1 1(2) Series and parallel connections A circuit usually contains many devices connected in different fashions. Two basic types of configuration are series and parallel. As shown in the figure below, when the devices are connected in series, the current going through them is the same (I = I1 = I2), and the total voltage across both devices is the sum of the voltage across each device (V = V1 + V2). However, for parallel connection, the voltage across the devices is the same (V = V1 = V2) since they share the same nodes across which the potential drop is measured, and the total current running through all the devices is the sum of the current in each branch (I = I1 + I2). V1 V2 Series : I1 I2 I Device 1 Device 2 + V _ I = I1 = I2 V = V1 + V2 Parallel : V1 I1 Device 1 I2 V2 Device 2 I + V _ I = I1 + I2 V = V1 = V2 Figure 2 Now let us examine the resistive circuits shown below. I1 V1 I1 Series : V1 I2 V2 I Parallel : R1 R1 R2 V I2 V2 I R2 V (a) (b) Figure 3 2_ In (a), based on Ohm’s law, V1 = R1I1, V2 = R2I2 And since this is a series connection, I1 = I2 = I, V = V1 + V2 Therefore, V = (R1 + R2) I Voltage-divider circuit: It is straightforward to get V1 ! R1 V R1 " R2 and V2 ! R2 V . R1 " R2 Therefore, when a voltage is applied to a series combination of resistances, a fraction of the voltage appears across each of the resistances. And of the total voltage, the fraction that appears across a given resistance in a series circuit is the ratio of the given resistance to the total series resistance. In (b), the two resistors are connected in parallel. From Ohm’s law, V1 = R1I1, V2 = R2I2 And since this is a parallel connection, V1 = V2 = V, I = I1 + I2 Therefore, I = V / R1 + V / R2 = R1R2V / (R1 + R2) Current-divider circuit: It is straightforward to get I1 ! R2 I R1 " R2 and I 2 ! R1 I R1 " R2 Therefore, the total current flowing into a parallel combination of resistances divides, and a fraction of the total current flows through each resistance. And the fraction of the total current flowing in a resistor is the ratio of the other resistance to the sum of the two resistances. (3) Ideal voltage and current sources An ideal voltage source supplies a constant voltage across its output terminals no matter how much current is going through it. Likewise, an ideal current source will supply constant current out no matter what the voltage across it is. The circuit symbol of the ideal voltage or current source is shown in the figure below. ideal voltage source ideal current source V + I Figure 4 3(4) Resistor The resistor is the most basic and widely used component in electronic circuits. And the relation of the voltage and the current of a resistor in a circuit will follow Ohm’s law. A typical resistor is color coded to indicate the resistance value. There are two types of color coding, 4-band-code and 5-band-code. As can be seen, the 5-band-code has one more digit resolution than the 4-band-code. The following chart provides the color code for both 4-band and 5-band resistors. To decode the color bands and calculate the corresponding resistance value, one needs to follow the steps below. a. Find the tolerance band. It is located at one end of the resistor and far away from the rest of the color bands. It gives the accuracy of the actual resistance to the value that is labeled. b. Start from the other end and use the color code map to identify the color band. This will be the first digit (the most significant digit) of the resistance value. c. Then similarly decode the second and the third band (for 5-band resistor only). Write down all the digits in order (from left to right). d. The last band is the multiplier. Use the decoded digits to multiply the decoded multiplier to get the resistance value. (5) Light emitting diode (LED) A diode is a basic but very important device that has two terminals, the anode and the cathode. Current can ONLY flow from anode to cathode, and NOT the other way around. The circuit symbol for a diode is shown in the (a) figure below, indicating the polarity. The simple piecewise-linear model approximates a 4diode’s I-V characteristic and is shown in (b). When the voltage applied across the diode is higher than a certain threshold value VTH, the diode is on, and the voltage across it stays fixed at the threshold value. However, if the voltage is lower than VTH, the diode is off, and there is no current going through the device. The actual diode I-V characteristic is shown in (c). Even though it does not
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