today: dc circuits mostly current & resistance
TRANSCRIPT
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today: dc circuits
mostly current & resistance
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not so funny now.
just wait ...
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battery = pumpvoltage = pressure
current = flowresistor = constriction
capacitor = diaphragm / flexible reservoirdiode = check valve
inductor = paddle wheel
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real V source = ideal V source + R
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actual circuit has a parasitic r
R in series with output(“steals” V)
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real current sources
R in parallel with output(“steals” I)
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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
-+
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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
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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 = +
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rank the currents
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THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
more complex arrangements
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measuring voltage
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real voltmeters
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measuring current
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a simple ammeter
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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
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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
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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
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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
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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?
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
Rules for analyzingmore complicated
circuits
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THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
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THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
+
+
+
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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
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THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center
combinations of capacitors
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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
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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
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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, }
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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)}
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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
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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
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ac capacitive circuitsI and V 90o out of phaseaverage power is ZERO
frequency response?insulating at dcconducting at high f
voltage “lags” current
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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
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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
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audio crossovers
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dB/decade ...
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+-
+Vcc
-Vcc
100k
photo-diode
+Vcc
741
741 pinout
output
Today:amplify photodiode signal