today: dc circuits mostly current & resistance

today: dc circuits

mostly current & resistance

not so funny now.

just wait ...

battery = pumpvoltage = pressure

current = flowresistor = constriction

capacitor = diaphragm / flexible reservoirdiode = check valve

inductor = paddle wheel

real V source = ideal V source + R

actual circuit has a parasitic r

R in series with output(“steals” V)

real current sources

R in parallel with output(“steals” I)

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

series resistors: conservation of energy

-+

R2

I I

∆V

R1a cbReq

∆V

a c

-+

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

voltage divider

R2

R1Vin Vout

Vout = R2

R1+R2Vin

signal in signal

out

R1

R2

volume

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

parallel resistors: conservation of charge

current divider

I

-+

R1

∆V

R2

a bI1

I2

∆V1=∆V2=∆V

-+

Req

∆V

Req R1 R2

1 11 = +

rank the currents

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

more complex arrangements

measuring voltage

real voltmeters

measuring current

a simple ammeter

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

dc Circuits, part II

same thing, just more of it

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

Thévenin equivalents

any combination of R’s and V’sis equivalent to a SINGLE R and V

(Norton equivalent: a single I source in parallel with R)

Vth = V (open circuit)

Rth = V (open circuit)

I (closed circuit)

disconnect from red dots = open circuit voltageshort red dots, current there is closed-circuit current.

This image: Horowitz & Hill, The art of electronics

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

series resistors: conservation of energy

-+

R2

I I

∆V

R1a cbReq

∆V

a c

-+

source voltage = sum of voltages on resistors

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

parallel resistors: conservation of charge

current divider

I

-+

R1

∆V

R2

a bI1

I2

∆V1=∆V2=∆V

-+

Req

∆V

Req R1 R2

1 11 = +

source current = sum of currents in resistors

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

so what?

V

R

real sources = ideal sources + R

real meter = ideal meter with

R

VI R

what about ammeter?

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

V source loading

V

r

source

extra seriesresistance

Rload

∆Vload = V - Ir

for r ≪ Rload, ∆Vload ≈ V

V source wants R high

one solution:large resistor in parallel with load

I

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

Ip

I source loading

source

extra parallelresistance

Rload

I source wants R lowsourcing currents at high Rload is hard

Ir

Iload

Iload = Ir

r+R

for Rload ≪ r, Iload ≈ I

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

measuring the meter

Rload

I

Vr

realmeter

Req

I

V

idealmeter

∆Vload = IReq = R1+R/rI Rload ≪ r, ∆Vload ≈ IR

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

summaryvoltmeter wants R low!can use a buffer/follower ... later

I source wants R lowtransformer pre-ampconsider sourcing V

V source wants R highlarge series + parallel resistorspresent large R

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

Sourcing current

Rwires

Rwires

RthingI V

This is what a hand meter does.

Why is it no good?

Vmeter = I(Rthing + 2Rwires)

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

Sourcing current, properly

No problem.You just need four wires.

Rwires

Rwires

Rthin

g

I V

Rthing ≪ Rinternal

or add buffer

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

Sourcing voltage

Rwires

Rwires

RthingVs

Still have to measure voltage on devicethe wires still use up some of V

What about current?

V

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

Sourcing voltage better

R = ∆V / I

Note we need 4 wires againcurrent meter - not hardstill problems?

Rwires

Rwires

Rthing

Vs

V

ΙΙ

=Rprecise

V

Rs

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

source/meter resistances

voltmeter wants R lowbut V source wants R high

need buffer/amp on V meter resistor in parallel with source

if V source is problem, R is too lowconsider sourcing I

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

what if I want to measure a *really* high R?

Rwires

Rwires

Rthing

Vs V

Ι

=Rs ≪ Rthing

Rp

Ι

=

V

source voltageRp has same voltage as Rthing

Rs has same current

have done >1010 Ohm

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

what if I want to measure a *really* low R?

Rwires

Rwires

Rthin

g

I V

this works just fine ...so long as your V meter is good or you can tolerate large Iv. good amp / part of a bridge

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

what if I want to measure a small change in R?

V

R1 R3

R2 Rx+dR

Vs

balance bridge to V=0detect small changes from null

make R1-R3 about the sametrimming resistor on R2 = dR

R2 =

≈ R3

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

Rules for analyzingmore complicated

circuits

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

+

+

+

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

capacitors

frequency-dependent resistorI and V are 90o out of phasecan’t dissipate power, ideally

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

combinations of capacitors

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

capacitors with stuff inside

Q0

+-

C0

∆V0

Q0

+-

Dielectric

C0

∆V

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

rc circuits

R

C

S

V ∝ e-τ/RC

VE

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

RC differentiatorC

Vin (t) Vout (t)R

for small RC, }

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

RC integrator

CVin (t) Vout (t)

R

for large RC (V ≪ Vin)}

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

so what?

filtering of signals

unintentional capacitive couplingsee from waveform shape

more later

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

ac resistive circuits

nothing earth-shattering happens

except P is lower than you expect

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

ac capacitive circuitsI and V 90o out of phaseaverage power is ZERO

frequency response?insulating at dcconducting at high f

voltage “lags” current

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

filters

C

RVin Vout

low-pass

CVin Vout

R

high-pass

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

familiar?

low-pass filter

C

RVin Vout

CVin Vout

R

high-pass filter

differentiatorintegrator

frequency domain⇕

time domain

audio crossovers

dB/decade ...

+-

+Vcc

-Vcc

100k

photo-diode

+Vcc

741

741 pinout

output

Today:amplify photodiode signal