diode and resonant circuits.ppt
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Lecture notes on Diodes and Resonant CircuitsTRANSCRIPT
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Parallel LC Resonant Circuit• Consider the following parallel LC circuit:
– Treating as a voltage divider, we have:
– Calculate the (complex) impedance ZLC:
R
C
Vin Vout
L(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)
inout VZR
ZV
LC
LC
LCj
j
C
LjZZZ CLLC
11111
LC
Lj
CL
jZLC 211
(Lab 3–1)
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Parallel LC Resonant Circuit• Thus we have:
– Note that for (resonant frequency):
– Otherwise is small
LC
L
LC
L
LC
Lj
LC
LjZLC 222
2
22 1111
22
22
22111 LC
LR
LC
LjR
LC
LjRZR LC
2222
22
222in
out
1
11 LCRL
L
LC
LRLC
L
V
V
LC
10 1
in
out V
V
in
out
V
V (Remember that = 2f)
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Parallel LC Resonant Circuit• Overall response (Vout / Vin vs. frequency):
– This circuit is sometimes called a tank circuit– Most often used to select one desired frequency from a
signal containing many different frequencies• Used in radio tuning circuits• Tuning knob is usually a variable capacitor in a parallel LC circuit
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)
Q = quality factor = f0 / f3dB = resonance frequency / width at –3 dB points
(Remember that at –3 dB point, Vout / Vin = 0.7 and output power is reduced by ½ )
Q is a measure of the sharpness of the peak
For a parallel RLC circuit: RCQ 0
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Oscillation in Parallel LC Resonant Circuit
(Introductory Electronics, Simpson, 2nd Ed.)
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Oscillation in Parallel LC Resonant Circuit• For a pure LC circuit (no resistance), the current and
voltage are exactly sinusoidal, constant in amplitude, and have angular frequency– Can prove with Kirchhoff’s loop rule– Analogous to mass oscillating on a spring with no friction
• For an RLC circuit (parallel or series), the current and voltage will oscillate (“ring”) with an exponentially decreasing amplitude– Due to resistance in circuit– Analogous to damped
oscillations of a mass on a spring
LC
10
(Introductory Electronics, Simpson, 2nd Ed.)
(Lab 3–1)
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Series LC Resonant Circuit• Consider the following series LC circuit:
– Now ZLC = ZC + ZL = jL – j / C (L and C in series)
• Overall response:
inout VZR
ZV
LC
LC
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)
R
L
f
fQ 0
dB3
0
For series RLC circuit:
(HW #1.26)
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Fourier Analysis• In Lab 3–1, a parallel LC resonant circuit is used as a
Fourier Analyzer– The circuit “picks out” the Fourier components of the input
(square) waveform
• Fourier analysis: Any function can be written as the sum of sine and cosine functions of different frequencies and amplitudes– We can apply this technique to periodic voltage waveforms:
– Where T = minimum time voltage waveform repeats itself and 1 / T = fundamental frequency = f0
– Could instead substitute T
1 1
0 2sin
2cos
2)(
n mmn T
mtb
T
nta
atV
(Lab 3–1)
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Fourier Analysis• The an and bm constants are determined from:
• For a symmetric square wave voltage (assuming V(t) is an odd function):– an = 0 n = 0, 1, 2, 3, …
–
–
2/
2/
cos)(2 T
T
n dttntVT
a
2/
2/
sin)(2 T
T
m dttmtVT
b
2/
0
sin)(4 T
m dttmtVT
b odd
4
even0
0 mm
V
mbm
...
5
5sin
3
3sin
1
sin4)( 0 tttV
tV
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Fourier Analysis• Thus for a square wave of fundamental frequency 0:
– When we apply an input square wave voltage of frequency 0to the parallel LC circuit, we are in essence applying frequencies , etc. simultaneously with relative amplitudes 1, 1/3, 1/5, etc. (respectively)
– The LC circuit is a “detector” of its resonance frequency f0, including contributions from the harmonics of the input fundamental frequency
• “Mini-resonance” peaks will occur in the output voltage at driving frequencies of f0 / 3, f0 / 5, etc.
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)
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Diodes• Diodes are semiconductor devices that are made when p–
type and n–type semiconductors are joined together to form a p–n junction– With no external voltage applied, there is some electron
flow from the n side to the p side (and similar for holes), but equilibrium is established and there is no net current
(Introductory Electronics, Simpson, 2nd Ed.)
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Diodes• With a reverse bias external voltage applied, there is only a
small net flow of electrons from the p side to the n side, and hence a small positive current from the n to the p side
(Introductory Electronics, Simpson, 2nd Ed.)
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Diodes• With a forward bias external voltage applied, electrons are
“pushed” in the direction they would tend to move anyway, and hence there is a large positive current from the p side to the n side
(Introductory Electronics, Simpson, 2nd Ed.)
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Diodes• Thus diodes pass current in one direction, but not
the other
• The diode’s arrow on a circuit diagram points in the direction of current flow
When diodes are forward-biased and conduct current, there is an associated voltage drop of about 0.6 V across the diode (for Si diodes) – “diode drop”
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)
Current can flow
Current can’t flowX
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Diodes in Voltage Divider Circuits• Consider diodes as part of the following voltage-
divider circuits:
(1)
• This diode circuit is called a rectifier (specifically, a half-wave rectifier)
Vin
Vout
(Lab 3–2)
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Diodes in Voltage Divider Circuits(2)
• This circuit is called a diode clamp circuit because the output voltage is “clamped” at about –0.6 V
Vin
Vout
(Lab 3–6)
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Diodes in Voltage Divider Circuits(3)
• This is another clamp circuit: the output voltage is clamped at about +5.6 V and –0.6 V
Vin
Vout
(Lab 3–6)
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Diode Applications• Rectification: conversion of AC to DC voltage
– We already saw how this could be done with a half-wave rectifier
– A much better way is with a full-wave bridge rectifier:
– Two diodes are always in series with the input (so there will always be 2 forward diode drops)
– Gap at 0 V occurs because of diodes’ forward voltage drop
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)
(Lab 3–3)
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Diode Applications• Although more efficient than the half-wave rectifier,
the bridge rectifier still produces a lot of “ripple” (periodic variations in the output voltage)– The ripple can be reduced by attaching a low-pass filter:
– The resistor R is actually unnecessary and is always omitted since the diodes prevent flow of current back out of the capacitors
– C is chosen to ensure that RloadC >> 1 / fripple so the time constant for discharge >> time between recharging
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)
(Lab 3–4)
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Diode Applications• We have almost finished building our own DC power
supply!• For further power supply design details, see Class 3
Worked Example in the Lab Manual (p. 71–74)
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)
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Diode Applications• Signal rectifier
– Eliminates an unwanted polarity of a waveform– Example: Remove sharp negative spikes from the output
of a differentiator– An RC differentiator is used to generate the spikes, and a
diode is used to rectify the spikes:
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)
(Lab 3–5)
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Diode Applications• Voltage limiter
– In the circuit below, the output voltage is limited to the range –0.6 V Vout +0.6 V
– This is just another example of a diode clamp circuit– Useful as an input protection circuit for a high-gain
amplifier (otherwise amplifier may “saturate”)
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)
(Lab 3–7)
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Example Problem: Chap. 1 AE 7
Sketch the output for the circuit shown at right. (Solution details will be discussed in class.)