• Homework• Quiz 3• Student

Perspective• System of

Equations• Bode Plots

Examples• Module IV

Announcements

No more Pre- Lab Module Homework

(Pre-Lab for Module V cancelled)

New Report Template (short and simple) – apply to Module III

New Report Rubric – apply to Module III

Homework-due 2/27 (Najera), due 3/2 (Quinones)

P15 and P16

Pre-Lab Module IV

Module IV: Build and Analyze 3 types of filters.

SUCCESS POINTS:

• REPORT WRITING –

CHECK TO MAKE SURE

EVERYTHING YOU SAY

REFER DIRECTLY TO

YOUR TABLES AND

GRAPHS?

P15 – Questions?

P15. (a) Determine the cut-off frequency for the low-pass filter shown below. Include all units and unit conversions for full credit. (b) If a signal frequency is increased to 10 kHz, will its amplitude be diminished or will it remain intact as it is processed by the filter?

• WHERE SHOULD CH1+

BE PLACED?

• HOW CAN YOU

DETERMINE THE CUT-

OFF FREQUENCY FOR

THIS CIRCUIT IN THE

LAB?

P16 – Questions?

P16. Assume that the circuit below has reached equilibrium and that the capacitor is fully charged. (a) Determine the value of VA, (b) the current flowing through R1, R2 and R3, and (c) the power consumed by R3. Show all equations required to solve this problem, all units, and all unit conversions for full credit.

VA

R1

R2 R3

Team Exercise

P16. Assume that the circuit below has reached equilibrium and that the capacitor is fully charged. (a) Determine the value of VA, (b) the current flowing through R1, R2 and R3, and (c) the power consumed by R3. Show all equations required to solve this problem, all units, and all unit conversions for full credit.

• REWORK THIS

PROBLEM WITH YOUR

TEAM ASSUMING:

• V = 20 V

• R1 = 25 k

• R2 = 1 M

• R3 = 500 k VA

R1

R2 R3

Quiz 3 – Power Calculations (20 pts)

• Please clear desks and turn off phones and put them in back packs

• You need pencil, straight edge and calculator

• 15 minutes

• Keep eyes on your own paper

• Follow same format as for homework

READ

INSTRUCTIONS

CAREFULLY!!!

Student Response to Module IRead each item carefully. Using the scale below, please circle the number that best describes the reason why you were ENGAGED IN THE MODULE I ACTIVITY in the lab. Answer each item according to the scale below.

1 - corresponds not at all

2 - corresponds a very little

3 - corresponds a little

4 - corresponds moderately

5 - corresponds enough

6 - corresponds a lot

7 - corresponds exactly

https://survey.az1.qualtrics.com/jfe/form/SV_emkJ9PDi3jmVEt7

YOUR OPINION

MATTERS.

Introduction to Kirchhoff’s Current Law and Kirchhoff’s Voltage Law

Key Method to Analyze Circuits

Applies to all Circuits

Sometimes result is a System of Equations

KCL

KVL

System of Equations Calculations

Adding Equations

Cramer’s Rule

Calculator/Computer

WHY DO WE

NEED TO SOLVE

A “SYSTEM OF

EQUATIONS”?

xxKCL: Kirchhoff’s Current Law

Sum of all Currents entering a node is equal to zero, where all currents entering a node are positive.

I1 = 5 A

I2 = 3 A

I3 = ?

I1 + I2 + I3 = 0

I3 = – 8 A

5A + 3A + I3 = 0

Source: Ulaby and Maharbiz, Circuits, Tech and Science Press, 2013.

xxKCL: Kirchhoff’s Current Law

Sum of all Currents entering a node is equal to zero, where all currents entering a node are positive.

Since I3 = – 8 A

can sketch direction of current in opposite direction

I1 = 5 A

I2 = 3 A

I3 = 8

I1 = 5 A

I2 = 3 A

I3 = ?

Source: Ulaby and Maharbiz, Circuits, Tech and Science Press, 2013.

xxKCL: Kirchhoff’s Current Law

I1 + I2 = I3

I3 = 8A

5A + 3A = I3

Sum of all Current entering a node is equal to the Sum of all Current leaving the node.

I1 = 5 A

I2 = 3 A

I3 = ?

I1 = 5 A

I2 = 3 A

I3 = ?

I1 + I2 + I3 = 0

Source: Ulaby and Maharbiz, Circuits, Tech and Science Press, 2013.

xxKVL: Kirchhoff’s Voltage LawSum of all voltages around a closed loop is equal to zero, where voltage drops are considered positive and voltage rises are considered negative. Imagine the redand black lines are leads from a voltmeter measuring voltage drops.

+ - V is positive or is a voltage drop

- +

V

V is negative or is a voltage riseV

Measuring from left to right

Source: Ulaby and Maharbiz, Circuits, Tech and Science Press, 2013.

xxKVL: Kirchhoff’s Voltage LawSum of all voltage around a closed loop is equal to zero, where voltage drops are considered positive and voltage rises are considered negative. Imagine the red and black lines are leads from a voltmeter measuring voltage drops.

-12V + 1.3 V + 4.03 V + 6.67 V = 0

KVL

+ -

Positive (+) Voltage Drop

- +

Negative (-) Voltage Drop

𝑛=1

𝑁

𝑉𝑛 = 0

xxKCL and KVL Example

Use KCL and KVL to determine I1, I2 and I3.

KVL:

Loop 1: -12 - 5000*I2 = 0

Loop 2: -12 - 5000*I3 = 0

Loop 3: - 5000*I3 + 5000*I2 = 0

KCL: I1 + I2 + I3 = 0

I2 = 12 𝑉

−5000

𝐴𝑉

= - 0.0024 A

I1 +(-0.0024 A) + (-0.0024 A) = 0.0048 A

You can assume the direction of current, if you get a negative value for that current, that means it is in the opposite direction.

I3 = 12 𝑉

−5000

𝐴𝑉

= - 0.0024 A

I1

I2

I3

xxKCL and KVL Visualization

xxKCL Example

Write the expression for KCL at node for two resistors in series to prove that they have the same current.

I1 I2

A

𝐾𝐶𝐿:

𝐼1 + 𝐼2 = 0

𝐼1 = 𝐼2

THESE RESISTORS ARE IN SERIES SINCE THERE IS NO ALTERNATE PATH BETWEEN THEM AT NODE A, AND…

xxKVL Team Exercise I

(a) Write the equation for KVL for the circuit below in terms of V1 and V2.

(b) Use Ohm’s Law to write equations for current (I) passing through R1 and R2 in terms of V1 and V2 to current (I).

(c) Substitute the equations from part (b) into part (a) and solve for the current (I).

(d) Find the power for each element in the circuit and prove the power is conserved for the circuit I

V1

V2

+ - +-

xxKVL Team Exercise II

(a) Write the expression for KVL for the circuit below, and (b) determine the value of the current (I).

I

EX:, THE KVL TERM FOR

THE 100 RESISTOR

WOULD BE 100 * I

xxKVL Team Exercise II

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=

System of Equations: Adding Equations

103𝑚𝐴

𝐴=

System of Equations: Adding Equations

•

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

Homework-due 3/6 (Najera), due 3/9 (Quinones)

P17 and P18SUCCESS 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 8?

Will introduce…

LAB• Module IV: EKG Sensor

LECTURE • System of Equations – Cramer’s Rule

• KCL and KVL

• Active Component Op-Amp Theory

Please bring laptops to all lectures and labs.

Questions?