Energy transfer with a resistor An emf E 1 with a higher voltage can - - PowerPoint PPT Presentation

William Sandqvist william@kth.se

Energy transfer with a resistor

An emf E1 with a higher voltage can charge an other emf E2 with a lower voltage if you connect them to together with a current limiting resistor. E1>E2.

1

E

2

E R E E I

2 1 −

= During charging, there becomes heat losses in R. It E W

1 1 =

It E W

2 2 =

t RI WR

2

=

The delivered energy Stored energy

I R

William Sandqvist william@kth.se

Energy transfer with an inductor

2 1

E E >

2 1

E E < With an inductor one can transfer energy from a larger emf to a smaller, E1>E2, Step Down, but also from a smaller emf to a larger, E1<E2, Step Up. This in theory is completely without losses. L

1

E

2

E

William Sandqvist william@kth.se

Step Up

1

E

2

E

2 1

E E < L

• Transistor
• Diode
• PWM-unit

Transistor and diode acts together as a switch controlled by the PWM unit.

Pulse width modulation

William Sandqvist william@kth.se

Step Up

1

E

2

E

1

E

2

E 2 1

E E <

i i L L

• n

t

• ff

t

• ff
• n
• n

t t t D + =

• DutyCycle D :

The coil current inertia

William Sandqvist william@kth.se

L E dt di dt di L E = ⇔ = The inductor has current-inertia. The current can not change

• immediately. A fluid analogy: The inductor is a water mill

with a flywheel. E i L t i L E = t Ψ

Pump Waterwheel Flywheel

Energy transfer with an inductor

William Sandqvist william@kth.se

L E1 I

max

I

avg

I i t L

1

E

2

E

• n

t Let E1 drive an increasing current through L during

• ton. The current then

reaches Imax.

• n

i

• n

i

Energy transfer with an inductor

William Sandqvist william@kth.se

L E E

2 1 −

I

max

I

avg

I i t L

1

E

2

E

• ff

t switch the inductor so that L now continnues the current through E2. E2>E1 means that the current will be decreasing. It will reach I0 again after time toff .

• ff

i

• ff

i The times ton, toff are those that gives us a stationary plot.

Energy transfer with an inductor

William Sandqvist william@kth.se

I

max

I

avg

I i t

• ff

i L E E

2 1 −

L E1

• n

i

• n

t

• ff

t

Stationary

Energy:

• ff
• n
• ff

avg 2 1

• ff
• n

avg 1

• n

) ( W W t I E E W t I E W = ⋅ ⋅ − = ⋅ ⋅ = D E E D t t t E E − ⋅ = − = + = 1 1 1 1

1 2

• ff
• ff
• n

1 2

5V → 50V ?

William Sandqvist william@kth.se

% 90 50 5 1 1 1 1

2 1 1 2

= − = − =

• −

⋅ = E E D D E E

5V

L

50V

1

E

2

E

Resistiv load?

William Sandqvist william@kth.se

5V

L

50V C

The current to the load will flow intermittently only during toff, so the voltage needs to be smoothed with a capacitor C.

( What is a diode? )

William Sandqvist william@kth.se

Semiconductor diode Symbol and characteristic Fluid Analogy check valve

A K

ideal diode blocking direction conduction direction

( What is a transistor? )

William Sandqvist william@kth.se

100 ≈ =

FE B C FE

h I I h

B C E The classic bipolar transistor, is earlier development than the MOS transistor. A small "base current"IB can control up to 100 times (hFE) bigger ”collector current” IC.

Fluid analogy mA 100 mA 1 =

• >

C B

I I PIC

Practical dimensioning?

William Sandqvist william@kth.se

It is simple to set up the Step-up converter's output voltage with the DutyCycle D! This we do at the lab. In practice it is much more difficult. An electronics engineer is faced with many questions: At what current "saturate" the coil iron core? How big internal resistance has the inductor? How big are the load variations? What values to L and C and f should be choosen? It is common to simulate the circuit with more realistic component models than what we use here. LT:s App note has the title ”Switching Regulators for Poets”

A problem is that while everyone agrees that working switching regulators are a good thing, everyone also agrees that they are difficult to get working. Unfortunately, switching regulators are one of the most difficult linear circuits to design. Mysterious modes, sudden, seemingly inexplicable failures, peculiar regulation characteristics and just plain explosions are common occurrences. Diodes conduct the wrong way. Things get hot that shouldn’t. Capacitors act like resistors, fuses don’t blow and transistors do. The output is at ground, and the ground terminal shows volts of noise. … Jim Williams

William Sandqvist william@kth.se

William Sandqvist william@kth.se

Jim Williams at lab

Simulation

William Sandqvist william@kth.se

D = 86 % Startup Sequence 0…1ms Simulation with an ideal switch

The voltage is stepping upwards…

5

1 =

E

Simulation

William Sandqvist william@kth.se

Stationary at 100 ms E1 = 5V E2 ≈ 30V D = 86% 30

2 ≈

E 5

1 =

E

William Sandqvist william@kth.se