homework kcl/kvl review bode plots active filters · what is a bode plot? a bode plot consists of:...
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• Homework• KCL/KVL Review• Bode Plots• Active Filters
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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?
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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
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System of Equations: Adding Equations
BASED ON THESE
EQUATIONS, CURRENT HAS
UNITS OF AMPS (A)
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System of Equations: Adding Equations
𝐴 103𝑚𝐴
1 𝐴=
I1 =5
1500I1 = 0.00333 𝐴
1500 𝐼1 = 5
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System of Equations: Adding Equations
103𝑚𝐴
𝐴=
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System of Equations: Adding Equations
•
I1=3.33 mA
I2=1.67 mA
I3=1.67 mA
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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
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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.
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xxKVL/KCL: In-Class Exercise
Using the KCL method, find I1 and I2.
Source: Ulaby and Maharbiz, Circuits, Tech and Science Press, 2013.
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xxKVL/KCL: In-Class Exercise
Using the KCL method, find I1 – I3.
Source: Ulaby and Maharbiz, Circuits, Tech and Science Press, 2013.
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When have circuits with AC signals, can analyze with
Bode Plot
(Magnitude vs Frequency)
Example: Filters
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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
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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
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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
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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?
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Bode Plots
Image Source: http://www.jensign.com/Discovery/bode/
LOW PASS FILTER HIGH PASS FILTER
20 dB PER DECADE
20 dB PER DECADE
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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)
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xxLocation of the 4 Op-Amps on your LMC6484 chip.
Op-Amp Chip (LMC6484 Op-Amp)
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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)
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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)
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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)
+ -
+ -
+-
+-
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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 +
-
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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
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xxVoltage Follower or Buffer
Used to isolate two circuits
Input Voltage
Output VoltageVoltage = Input Voltage
Input Voltage
No Current
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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
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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:
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xxInverting Amplifier𝑽𝒐𝒖𝒕
𝑽𝒊𝒏= −
𝑹𝟐
𝑹𝟏𝒘𝒉𝒆𝒓𝒆 𝒕𝒉𝒆 𝑮𝒂𝒊𝒏 = −
𝑹𝟐
𝑹𝟏
WHAT IS THE APPROXIMATE RELATIONSHIP BETWEEN R1 AND R2?
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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
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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 …
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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.
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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.
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Questions?