Homework KCL/KVL Review Bode Plots Active Filters

Transcription

1 Homework KCL/KVL Review Bode Plots Active Filters

2 Homeworkdue 3/6 (Najera), due 3/9 (Quinones) SUCCESS POINTS: REPORT WRITING CHECK TO MAKE SURE EVERYTHING YOU SAY REFER DIRECTLY TO YOUR TABLES AND GRAPHS? P17 and P18 Questions?

3 xx KVL/KCL Review Use KCL and KVL to determine the values of the currents I1, I2 and I3. I 1 I 2 I 3 THIS EXAMPLE SHOWS HOW TO DEVELOP A STRAGEDY TO SOLVE A SYSTEM OF EQUATIONS.

4 System of Equations: Adding Equations BASED ON THESE EQUATIONS, CURRENT HAS UNITS OF AMPS (A)

5 System of Equations: Adding Equations 1500 I1 = 5 I1 = I1 = A A 10 3 ma 1 A =

6 System of Equations: Adding Equations 10 3 ma A =

7 System of Equations: Adding Equations I 1 =3.33 ma I 3 =1.67 ma I 2 =1.67 ma

8 I 1 I 2 xx KVL/KCL: In-Class Exercise Use KCL and KVL to determine the values of the currents I1, I2 and I3. I 3 I 1 A I 3 I 2 B THIS EXAMPLE SHOWS HOW TO DEVELOP A STRAGEDY TO SOLVE A SYSTEM OF EQUATIONS.

9 xx KVL/KCL: In-Class Exercise Use KCL and KVL to determine I1 through I4. Label all steps. Source: Ulaby and Maharbiz, Circuits, Tech and Science Press, 2013.

10 xx KVL/KCL: In-Class Exercise Using the KCL method, find I 1 and I 2. Source: Ulaby and Maharbiz, Circuits, Tech and Science Press, 2013.

11 xx KVL/KCL: In-Class Exercise Using the KCL method, find I 1 I 3. Source: Ulaby and Maharbiz, Circuits, Tech and Science Press, 2013.

12 When have circuits with AC signals, can analyze with Bode Plot (Magnitude vs Frequency) Example: Filters

13 What is a Bode Plot? A Bode Plot consists of: ANGULAR FREQUENCY SYMBOL: UNITS: RADIANS/SECOND FREQUENCY SYMBOL: f UNITS: CYCLES/SECOND OR Hz Two plots used to interpret how the filter affects the input in terms of both magnitude and phase. x Axis: Logarithm scale of frequency on x axis for both plots (f or ) y Axis Plot 1: Magnitude in units of decibels (db) y Axis Plot 2: Phase angle in degrees Source:

14 Bode Plots ELIMINATES SIGNAL ABOVE fc Y AXIS db - DECIBELS ELIMINATES SIGNAL BELOW fc Y AXIS DEGREES LOW PASS FILTER HIGH PASS FILTER Image Source:

15 Bode Plots RECALL THAT THE BODE PLOT: ILLUSTRATES THE GAIN IN THE SIGNAL (INPUT VS OUTPUT), AND THE PHASE DIFFERENCE BETWEEN THE INPUT AND OUTPUT SIGNALS LOW PASS FILTER HIGH PASS FILTER Image Source:

16 Bode Plots WHAT IS THE DECREASE IN THE SIGNAL (OUTPUT VS INPUT) IN UNITS OF db (DECIBEL) PER DECADE IN FREQUENCY? EX. 1 DECADE WOULD BE BETWEEN Hz SO ON THE GRAPH, NEED TO DETERMINE HOW MUCH THE SIGNAL DECREASES IN db BETWEEN THESE FREQUENCY VALUES?

17 Bode Plots 20 db PER DECADE 20 db PER DECADE LOW PASS FILTER HIGH PASS FILTER Image Source:

18 xx Op-Amp Theory and Circuit Analysis An Op-Amp is an active device since it needs a power supply to operate. The Op-Amp has 2 inputs and 1 output. SYMBOL (normally don t show +Vss and Vss) How many pins are on the Op-Amp chip that we use? - 3 pins per Op-Amp, 12 pins total, plus 2 pins for +Vss and Vss, so 14 total pins Image source:

19 xx Op-Amp Chip (LMC6484 Op-Amp) Location of the 4 Op-Amps on your LMC6484 chip.

20 xx Op-Amp Chip (LMC6484 Op-Amp) Notice where the voltage connections are (V+ will be connected to 5V, and V- will be connected to ground). Therefore, orient the Op-Amp so you can connect easily to 5 V and ground.

21 xx Op-Amp Chip (LMC6484 Op-Amp) Notice that for each Op-Amp, the outputs are all at the corners of the chip. It does not matter which Op-Amp you use, as long as it is practical for your circuit design.

22 xx Op-Amp Chip (LMC6484 Op-Amp) Notice where the inverting (-) and non-inverting (+) inputs are for each Op-Amp on the chip, and that the inverting (-) input is always next to the output pins

23 xx Op-Amp Theory and Circuit Analysis Power Supply (Vcc not shown) R2 The inputs (non-inverting (+) and inverting (-) to the op-amp draw no current (i.e. i = 0 into both inputs). in R1 i=0 Vn - i=0 + Vp Vout The two input voltages values are equal to each other (Vn = Vp). Ex. If Vref is ground, then Vn = Vp = 0 V. One output, Vout. Vref OpAmp can saturate if Vout is greater than Vcc!!!! - more about this later

24 Can analyze with Complex Impedance Can analyze with KCL/KVL xx Op-Amp Theory and Circuit Analysis Types of Op-Amps we cover in this course: Voltage Follower or Buffer: Sets the voltage at that point in the circuit Inverting Amplifier: Inverts the signal horizontally, and amplifies the signal Non-Inverting Amplifier: Amplifies the signal Filter OpAmp: Filters the signal: low, high or band pass

25 xx Voltage Follower or Buffer Used to isolate two circuits No Current Voltage = Input Voltage Input Voltage Output Voltage Input Voltage

26 Key Review Question What information do you need to determine the current flowing through a resistor? The Resistor Value The Voltage Drop Across the Resistor

27 V out V in = R 2 R 1 where the Gain = R 2 R 1 xx Inverting Amplifier Vp = Vn = Vref = Grd = 0 R2 KCL: I 1 + I 2 = 0 (currents entering a node are zero) KVL: or I 1 = I 2 Vin V in V n R 1 = (V out V n ) R 2 R1 I 1 Vn I 2 Vp - + Vou V in R 1 = V out R 2 Vref = Ground

28 xx Inverting Amplifier V out V in = R 2 R 1 where the Gain = R 2 R 1 WHAT IS THE APPROXIMATE RELATIONSHIP BETWEEN R1 AND R2?

29 xx Circuit Exercise IV - Non-Inverting Op-Amp Assuming Vin = Vn and ip = in = O, use KCL to write an expression for Vout/Vin. Vin Vp ip=0 Vn in=0 Vout I 2 R2 = 25 k I 1 R1 = 10 k

30 xx Low Pass Filter C1 Where the gain of the Op-Amp is equal to Low Pass Filter R2 Gain = R 2 R 1 Vin R1 Vout Vref

31 Homeworkdue 3/20 (Najera), due 3/23 (Quinones) SUCCESS POINTS: TRY EXPLAINING HOW A BODE PLOT WORKS TO A TEAM MEMBER, AND THEN HAVE THEM EXPLAIN IT TO YOU. P19 and P20 Module V: Oxygen Sensor Operational Amplifier Build and analyze buffer, inverting amplifier, and photodiode oxygen sensor circuits.

32 What s Next in Week 10? Will introduce LAB Module V: Oxygen Sensor LECTURE Quiz 4 KCL and KVL Active Component Op-Amp Theory Please bring laptops to all lectures and labs.

33 Questions?