E40M Device Models, Resistors, Voltage and Current Sources, Diodes, - - PowerPoint PPT Presentation

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E40M Device Models, Resistors, Voltage and Current Sources, Diodes, - - PowerPoint PPT Presentation

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E40M Device Models, Resistors, Voltage and Current Sources, Diodes, Solar Cells M. Horowitz, J. Plummer, R. Howe 1 Understanding the Solar Charger Lab Project #1 We need to understand how: 1. Current, voltage and power behave in circuits

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  • M. Horowitz, J. Plummer, R. Howe

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E40M Device Models, Resistors, Voltage and Current Sources, Diodes, Solar Cells

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Understanding the Solar Charger – Lab Project #1

We need to understand how:

  • 1. Current, voltage and power behave in circuits
  • 2. Electrical devices constrain current and voltage
  • 3. Diodes including solar cells work
  • 4. Voltage converter works (later in the quarter).
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Reading For These Topics

  • Chapter 1 in the course reading
  • A&L 1.6-1.7 - Two terminal elements

– Voltage source; resistor; wires

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Key Ideas on KCL, KVL and Energy Flow - Review

i1 i2 i3 Kirchhoff’s Current Law (KCL) states that the current flowing out

  • f any node must equal the

current flowing in. So, for example, i1 = i2 + i3 Kirchhoff’s Voltage Law (KVL) states that the algebraic sum of the voltages around any closed path must be zero. So, for example, V1 + V2 – V3 = 0

+ + +

  • V1

V2 V3

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  • Find the power dissipated in each device
  • First figure out which lead has the higher voltage

– Then figure out whether current flows into or out of that lead

Key Ideas on KCL, KVL and Energy Flow - Review

+

  • 5V

1 A +

  • 2V
  • 1 A

+

  • 5V

1 A +

  • 1V

1 A

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  • A general way to show the relationship between two variables
  • That is what we will do for our different types of electrical devices

Device Models

i v i + , v + i - , v + i - , v - i + , v -

+

  • 5 V

1 A

Sign convention: positive current flows into the terminal with the + voltage label

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Device Models

  • Note that the energy is dissipated by the device in quadrants 1 and 3,

and power is generated by the device in quadrants 2 and 4.

i v i + , v + i - , v + i - , v - i + , v -

+

  • 5 V

1 A 1 2 3 4

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Device Models – Battery, Voltage Source

  • A battery or a voltage source provide a fixed out put voltage no matter

what current they are asked to provide or consume (“sink”).

  • In quadrant 1 energy is consumed, in quadrant 4 energy is provided.
  • Quadrant 1 = battery charging, quadrant 4 = battery discharging.

i

+ –

5 V

+

  • 5 V

v

1 2 3 4

i

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  • Current is proportional to voltage

V = i·R Ohm’s Law

  • The book also uses G

Conductance = 1/R i = G·V

  • Symbol

Device Models – Resistors

v i

+ –

V

i

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Why Does Resistance Exist? (What Physical Effect Does it Model?)

  • Conductors are not perfect

– They use a little energy to get current to flow through a wire1

  • Since the energy flow into the wire is (i ΔV)

– There must be a voltage drop along the wire – Generally this drop is proportional to the current

  • V = k · i
  • We call the constant of proportionality

“Resistance”

  • Make resistors by using material that doesn’t

conduct well

1Well except for superconductors which are “magical.” They have interesting properties, including that current can flow in a loop

forever! Superconductors are used in MRI machines to generate large magnetic fields efficiently.

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Resistors

http://ecee.colorado.edu/~mathys/ecen1400/labs/resistors.html

http://www.instructables.com/id/Reading-Surface-Mount-Resistor-codes/

  • You’ll begin to work with these this Friday

in the Prelab lecture.

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Resistance Problem #1

i = ? What current flows in the loop? What is the voltage across the bottom resistor?

1kΩ 1kΩ

+

1 V

–

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Resistance Problem #2

i = ? What is the current i?

+ –

1 V 1kΩ 1kΩ

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New Device: Current Source

  • Current is constant, independent of voltage; i is negative in this

case because it flows out of the + terminal

  • In quadrant 4 the current source is providing energy, in quadrant

3 the current source consumes energy. i v

4 3

i - , v + i - , v -

+ –

i

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New Device – Diode

  • Diode is a one-way street for current

– Current can flow in only one direction

  • An ideal diode

– If the current is positive

  • Voltage drop is zero independent of current
  • Looks like a wire (short circuit)

– If the voltage is negative

  • Current is always zero independent of voltage
  • Looks like the device is not there (open circuit)
  • The plus end of the diode is called the anode

– The minus end of the diode is called the cathode

v i

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There Are Many Types of Diodes

http://www.instructables.com/id/Types-of-Diodes/

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Real Diodes

  • Do conduct current in only one direction

– But they have some forward voltage drop – And their voltage does increase with current, but – Current is exponential on voltage! – and voltage is logarithmic on current. – So the voltage is not very dependent on current level

  • Their drop depends on the type of diode

– Schottky diodes are around 0.3 V – Normal silicon PN diodes are generally around 0.6 V – Other semiconductor materials have larger voltages

I = Io exp qV kT ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

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Diode iv

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

  • 3
  • 2.5
  • 2
  • 1.5
  • 1
  • 0.5

0.5 1

i

v

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Idealized Diode iv

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

  • 3
  • 2.5
  • 2
  • 1.5
  • 1
  • 0.5

0.5 1

Vf

i

v

  • This is the model we will mostly use in E40M

– Matches the behavior of a real diode pretty well – Just need to choose the right value of Vf

  • For any positive current

– The voltage drop across the diode is Vf

  • For any voltage less than Vf

– The current through the device is zero

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Diodes in Simple Circuits +

1 V

–

1kΩ

+

1 V

–

1kΩ Vf = 0.6 Vf = 0.6

i = ? i = ?

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Some Diodes Are Light Sensitive

  • These diodes are called solar cells
  • When you shine light on the cell

– The light generates a current which runs in parallel to the diode – The value of the current is proportional to the light

  • This generates electrical energy

– Actually converts energy in the light to electrical form

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Solar Cell

  • Remember a solar cell is a diode

– So we represent it by a diode symbol

  • When light shines on the diode

– The light generates a current – We represent this current by a current source.

  • The value of this current is

proportional to the light shining on the diode – Notice the direction of the current

  • Flows out of + terminal of diode
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Solar Cell i-V Curve

i V

  • 0.5
  • 0.3
  • 0.1

0.1 0.3 0.5 0.7 0.9

Optically generated current

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Open Circuit Voltage Short Circuit Current

  • What is the voltage when zero current flows out of the device?
  • What is the current when there is no voltage across the device?
  • 0.5
  • 0.3
  • 0.1

0.1 0.3 0.5 0.7 0.9

Short Circuit Current Open Circuit Voltage i v i

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What Sets the Open Circuit Voltage and the Short Circuit Current?

  • If there is no path for current (open source voltage

case) – It will flow into the diode – KCL must still hold – Vdiode = VF

  • If you short the diode out (short circuit current)

– You measure all the optically generated current

i

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Extracting Power from a Diode

  • Power is i ·V

– So in neither of these cases do we get power from the diode

  • Actual power will be less

than: – VOC, iSC

  • You’ll actually measure

these parameters on your solar array next week.

  • 0.5
  • 0.3
  • 0.1

0.1 0.3 0.5 0.7 0.9

Short Circuit Current Open Circuit Voltage i v

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FYI – How Do Light Emitting Diodes and Solar Cells Actually Work?

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Generating Enough Voltage

  • There is one weak point for solar cells

– Each cell provides < 0.5 V – We need around 5 V, so we bought a panel with many cells stacked in series

  • Commercial photovoltaic arrays also use this

approach

  • How do we figure out voltages and currents here?
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Or Here?

Solar Cell Li Bat Volt Conv

Diode R In the next set of lecture notes we’ll develop methods to analyze circuits by extending the KCL and KVL ideas we’ve already discussed.

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Learning Objectives for These Notes

  • Understand the device i-V curve of a resistor
  • Understand the device i-V curve of a voltage source
  • Understand the device i-V curve of a current source
  • Understand the operation of a diode, and its symbol