SMV ELECTRIC TUTORIALS Nicolo Maganzini, Geronimo Fiilippini, Aditya Kuroodi 2015 Relevant Course(s): EE10, EE11L 2 RESISTORS IN NETWORKS What are we learning? Learn about the math behind networks of resistors. Current and Voltage laws. Predicting/designing circuits that have specific values of Current, Voltage, Resistance Learn about some very important structures of networks Parallel and series How are they used? CAUTION: Math involved. 3 Resistors in Networks In Circuit Schematics: In Real Life: 4 Resistor Network Calculations - Series Networks You have this circuit: R1 = 1 Ohm, R2 = 2 Ohm, R3 = 3 Ohm, V = 6V How can you apply Ohm’s law to find out how much current is flowing? 5 Series Resistors Equation. This is called a series connection: Equivalent Resistance = R1 + R2 + R3 + R4 Since there is only one path for electrons, there is only one current value in the part of the circuit with the series connection. Try it yourselves! (next slide) 6 The circuit we’re building: R1 = 100 Ohm R2 = 220 Ohms R3 = 300 Ohms Battery = 9V Measure current at nodes 1,2. Write them down. Check that they are equal. Measure voltages V1(across R1), V2 (across R2), V3 (across R3), across the battery. Calculate: V1/R1, V2/R2, V3/R3 What should these be equal to? V1+V2+V3 What should this be equal to? (V1+V2+V3)/(R1+R2+R3) What should this be equal to? 7 Parallel Networks Current has multiple paths it can take. It will split according to the resistance in each path. Path with lower resistance gets most current. Path with higher resistance gets less current. If resistances are equal, all paths have the same current. 8 Let’s combine the two! Then add it to this one! This is in Parallel: Find it’s equivalent Split circuit between parallel and series parts. Simplify the parallel part and add it to the series part. Parallel part simplification: Overall equation for resistance: 9 Sample Problem Calculate the current flowing out of the battery in this circuit: R1 = 100 Ohms R2 = 150 Ohms R3 = 200 Ohms Battery = 9V 10 Kirchoff current and voltage laws How do we analyze more complicated circuits? There are some physics laws that we can apply to circuits that allows us to find equations: Kirchoff laws. Steps: 1) Apply Laws 2) Find Equations 3) Solve equations to find current, voltage and resistance. 11 Kirchoff Voltage Law (KVL) What the law says: The sum of all voltages in a loop must be equal to zero. Example of how we use it: Vbatt = 9V. V1 = 2V V2 = 3V R3 = 4 Ohms Find the current in the circuit. 12 Kirchoff Voltage Law (KVL) Step 1) Apply law: The voltage produced by the battery is equal to the voltage dropped by each resistor. Step 2) Find Equation: Vbatt = V1+V2+V3 Know Vbatt, V1, V2; Find V3 I = V3/R3 Know V3 and R3, Find I. Step 3) Solve: V3 = 9-2-3 = 4V I = 4/4 = 1A 13 Kirchoff Current Law (KCL) What the law says: The sum of all currents entering and exiting a node must be zero. Example of how we use it: R1 = 100 Ohms. R2 = 200 Ohms R3 = 200 Ohms. Current through R1 = 1A Find voltage of battery. 14 Kirchoff Current Law (KCL) Step 1) Apply Laws: Current flowing into node 2 from R2 and R3 must be equal to current flowing out towards R1. Current flowing in R2 and R3 must be equal because resistances are equal (200 ohm) Sum of voltages must be equal to the battery voltage Step 2) equations: I1 = I2 + I3 I2 = I3 V1+V2 = V1 + V3 = Vbattery Step 3) solve: 1 = ½ + ½ I2 = I3 = ½ A V1 = I1 R1 = 100V V2 = V3 = ½ x 200 = 100V Vbatt = 100 + 100 = 200V 15 Using series connections to make a sensor Potential divider equation: 𝑉𝑜𝑢𝑡 = 𝑉𝑏𝑎𝑡𝑡𝑒𝑟𝑦 𝑅2 𝑅1 +𝑅2 VERY IMPORTANT EQUATION. Pseudo-Derivation If Resistance values are constant, then Vout will be constant. What if the resistance of one resistor changes with temperature or light? How does Vout change? 16 CAPACITORS AND SIGNAL FILTERING Ohm’s Law for Capacitors Voltage across resistor depends on value of current at that instant in time: 𝑉 = 𝐼𝑅 Voltage across capacitor depends on how fast the current is changing: 𝑉 = 𝐼 𝑋𝑐 where 𝑋𝑐 = 1 = Capacitive 2𝜋𝑓𝐶 Reactance 𝑉 = 𝐼 2𝜋𝑓𝐶 V is maximum voltage across capacitor, I is maximum current through capacitor, C is capacitance, f is frequency of signal. 18 Low Pass Filter Remember potential divider equation? Voltage across R2 is given by: 𝑅2 1 +𝑅2 𝑉𝑜𝑢𝑡 = 𝑉𝑏𝑎𝑡𝑡𝑒𝑟𝑦 𝑅 1 Now substitute R2 with reactance 𝑋𝑐 = 2𝜋𝑓𝐶 Can you do it? 1 𝑉𝑜𝑢𝑡 = 𝑉𝑏𝑎𝑡𝑡𝑒𝑟𝑦 2𝜋𝑓𝐶𝑅+1 Increase resistance = lower 𝑉𝑜𝑢𝑡 Increase capacitance = lower 𝑉𝑜𝑢𝑡 Increase frequency = lower 𝑽𝒐𝒖𝒕 This is a LOW PASS FILTER. Can tune 𝑅 and 𝐶 to cancel out the right requencies. 𝑉𝑜𝑢𝑡 𝑉 High Pass Filter What if we turn around the circuit, so that capacitor is on the top? 𝐶 𝑅 𝑉 𝑅2 1 +𝑅2 𝑉𝑜𝑢𝑡 = 𝑉 𝑅 𝑉𝑜𝑢𝑡 1 substitute 𝑋𝑐 = 2𝜋𝑓𝐶 for 𝑅1 . Can you simplify it? This time low frequencies are attenuated This is a high pass filter. Note: if signal has f = 0, it is completely eliminated DC is blocked. Only signals that change in time make it through 20 R = 1 kOhm C = 0.22 microF What have we learned? If the signal has a certain frequency, we can make an R-C circuit that cancels the signal out. If a signal has more than one frequency, such as noise: Can clean it up using an R-C filter designed to cancel out all frequencies lower than a certain amount. 21