homework kcl/kvl review bode plots active filters · what is a bode plot? a bode plot consists of:...
TRANSCRIPT
• Homework• KCL/KVL Review• Bode Plots• Active Filters
Homework-due 3/6 (Najera), due 3/9 (Quinones)
P17 and P18
Questions?
SUCCESS POINTS:
• REPORT WRITING –
CHECK TO MAKE SURE
EVERYTHING YOU SAY
REFER DIRECTLY TO
YOUR TABLES AND
GRAPHS?
xxKVL/KCL Review
Use KCL and KVL to determine the values of the currents I1, I2 and I3.
THIS EXAMPLE SHOWS
HOW TO DEVELOP A
STRAGEDY TO SOLVE A
SYSTEM OF EQUATIONS.
I1
I2
I3
System of Equations: Adding Equations
BASED ON THESE
EQUATIONS, CURRENT HAS
UNITS OF AMPS (A)
System of Equations: Adding Equations
𝐴 103𝑚𝐴
1 𝐴=
I1 =5
1500I1 = 0.00333 𝐴
1500 𝐼1 = 5
System of Equations: Adding Equations
103𝑚𝐴
𝐴=
System of Equations: Adding Equations
•
I1=3.33 mA
I2=1.67 mA
I3=1.67 mA
xxKVL/KCL: In-Class Exercise
Use KCL and KVL to determine the values of the currents I1, I2 and I3.
THIS EXAMPLE SHOWS
HOW TO DEVELOP A
STRAGEDY TO SOLVE A
SYSTEM OF EQUATIONS.
I1
I2
I3
A
B
I1
I2
I3
xxKVL/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.
xxKVL/KCL: In-Class Exercise
Using the KCL method, find I1 and I2.
Source: Ulaby and Maharbiz, Circuits, Tech and Science Press, 2013.
xxKVL/KCL: In-Class Exercise
Using the KCL method, find I1 – I3.
Source: Ulaby and Maharbiz, Circuits, Tech and Science Press, 2013.
When have circuits with AC signals, can analyze with
Bode Plot
(Magnitude vs Frequency)
Example: Filters
What is a Bode Plot?
A Bode Plot consists of:
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: http://www.ece.utah.edu/~ee3110/bodeplot.pdf
ANGULAR FREQUENCY
SYMBOL:
UNITS: RADIANS/SECOND
FREQUENCY
SYMBOL: f
UNITS: CYCLES/SECOND
OR Hz
Bode Plots
Image Source: http://www.jensign.com/Discovery/bode/
LOW PASS FILTER HIGH PASS FILTER
ELIMINATES SIGNAL ABOVE fc
ELIMINATES SIGNAL BELOW fcY AXIS – dB - DECIBELS
Y AXIS – DEGREES
Bode Plots
Image Source: http://www.jensign.com/Discovery/bode/
LOW PASS FILTER HIGH PASS FILTER
RECALL THAT THE BODE PLOT:
• ILLUSTRATES THE GAIN IN THE SIGNAL (INPUT
VS OUTPUT), AND
• THE PHASE DIFFERENCE BETWEEN THE INPUT
AND OUTPUT SIGNALS
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 104 – 105 Hz
SO ON THE GRAPH, NEED TO DETERMINE HOW MUCH THE SIGNAL
DECREASES IN dB BETWEEN THESE FREQUENCY VALUES?
Bode Plots
Image Source: http://www.jensign.com/Discovery/bode/
LOW PASS FILTER HIGH PASS FILTER
20 dB PER DECADE
20 dB PER DECADE
xxOp-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.
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: http://elektronikadasar.info/wp-content/uploads/2013/01/OP-Amp.png
SYMBOL(normally
don’t show +Vss and –
Vss)
xxLocation of the 4 Op-Amps on your LMC6484 chip.
Op-Amp Chip (LMC6484 Op-Amp)
xxNotice 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.
Op-Amp Chip (LMC6484 Op-Amp)
xxNotice 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.
Op-Amp Chip (LMC6484 Op-Amp)
xxNotice 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.
Op-Amp Chip (LMC6484 Op-Amp)
+ -
+ -
+-
+-
xxOp-Amp Theory and Circuit Analysis Power Supply (Vcc – not shown)
The inputs (non-inverting (+) and inverting (-) to the op-amp draw no current (i.e. i = 0 into both inputs).
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.
OpAmp can saturate if Vout is greater than Vcc!!!! -more about this later
VinVout
Vref
Vn
Vp
R1
R2
i=0
i=0 +
-
xx
Types of Op-Amps we cover in this course:
Op-Amp Theory and Circuit Analysis
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
Can
an
alyz
e w
ith
K
CL
/KV
L
Can
an
alyz
e w
ith
C
om
ple
x Im
ped
ance
xxVoltage Follower or Buffer
Used to isolate two circuits
Input Voltage
Output VoltageVoltage = Input Voltage
Input Voltage
No Current
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
xxInverting Amplifier
Vin Vout
Vref = Ground
Vp
VnR1
R2
𝑽𝒑 = 𝑽𝒏 = 𝑽𝒓𝒆𝒇 = 𝑮𝒓𝒅 = 𝟎
KCL: 𝑰𝟏 + 𝑰𝟐 = 𝟎(currents entering a node are zero)
or
𝑰𝟏 = −𝑰𝟐
𝑽𝒊𝒏 − 𝑽𝒏
𝑹𝟏=
−(𝑽𝒐𝒖𝒕−𝑽𝒏)
𝑹𝟐
𝑉𝑖𝑛
𝑅1=
−𝑉𝑜𝑢𝑡
𝑅2
𝑰𝟏
𝑰𝟐
𝑽𝒐𝒖𝒕
𝑽𝒊𝒏= −
𝑹𝟐
𝑹𝟏𝒘𝒉𝒆𝒓𝒆 𝒕𝒉𝒆 𝑮𝒂𝒊𝒏 = −
𝑹𝟐
𝑹𝟏
-
+KVL:
xxInverting Amplifier𝑽𝒐𝒖𝒕
𝑽𝒊𝒏= −
𝑹𝟐
𝑹𝟏𝒘𝒉𝒆𝒓𝒆 𝒕𝒉𝒆 𝑮𝒂𝒊𝒏 = −
𝑹𝟐
𝑹𝟏
WHAT IS THE APPROXIMATE RELATIONSHIP BETWEEN R1 AND R2?
xxCircuit Exercise IV - Non-Inverting Op-Amp
Assuming Vin = Vn and ip = in = O, use KCL to write an expression for Vout/Vin.
VoutVp
Vn
𝑰𝟐
𝑰𝟏
Vinip=0
in=0
R2 = 25 k
R1 = 10 k
xxLow Pass Filter
R1
R2
C1
Vref
Vout
Vin
Low Pass Filter
𝑮𝒂𝒊𝒏 = −𝑹𝟐
𝑹𝟏
Where the gain of the Op-Amp is equal to …
Homework-due 3/20 (Najera), due 3/23 (Quinones)
P19 and P20
Module V: Oxygen SensorOperational Amplifier
Build and analyze buffer, inverting amplifier, and photodiode oxygen sensor circuits.
SUCCESS POINTS:
• TRY EXPLAINING HOW
A BODE PLOT WORKS
TO A TEAM MEMBER,
AND THEN HAVE THEM
EXPLAIN IT TO YOU.
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.
Questions?