Circuits to Small-signal ac equivalent circuit
Amplifier
• อัตราขยายแรงดันในหน่วยเดซิเบล (Voltage Gain in dB):
Gain in dB = 20 log |Av|
• อัตราขยายกระแสในหน่วยเดซิเบล (Current Gain in dB):
Gain in dB = 20 log |Ai|
• อัตราขยายกาลังในหน่วยเดซิเบล (Power Gain in dB):
Gain in dB = 10 log (Ap)
• เกนที่เป็ นค่าลบ (-dB) หมายถึงสัญญาณถูกลดทอน หรือมีการกลับเฟสสัญญาณ 180 องศา
Amplifier
Circuits to Small-signal ac equivalent circuit
Intrinsic Semiconductors
valence electron – is an electron that participates in the
formation of chemical bonds.
Atoms with one or two valence electrons more
than a closed shell are highly reactive because
the extra electrons are easily removed to form
positive ions.
covalent bond – is a form of chemical bond in which two
atoms share a pair of atoms.
It is a stable balance of attractive and repulsive
forces between atoms when they share electrons.
silicon atom
- four valence electrons
- requires four more to complete outermost shell
Figure 3.1 Two-dimensional representation of the silicon crystal.
- each pair of shared forms a covalent bond
- the atoms form a lattice structure
semiconductor – a material whose conductivity lies between that of conductors and insulators.
single-element – such as germanium and silicon.
compound – such as gallium-arsenide.
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Current Flow in Semiconductors
Drift Current
 What happens when an electrical field (E) is applied to a semiconductor crystal?
 Holes are accelerated in the direction of E, free electrons are repelled.
 How is the velocity of these holes defined?
.E (volts / cm)
.p (cm2/Vs) = 480 for silicon
. n (cm2/Vs) = 1350 for silicon
note that electrons move with velocity 2.5 times higher than holes
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Current Flow in Semiconductors
Diffusion current
• Carrier diffusion – is the flow of charge carriers from area of high concentration to low
concentration.
• Diffusion current – is the current flow that results from diffusion.
Figure 3.6: A bar of silicon
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3.5 The pn Junction with an Applied Voltage
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3.5 The pn Junction with an Applied Voltage
• Current is diffusion current - drift current
• At the edge x = xn, minority is hole carrier
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Terminal Characteristics of Junction Diode
The characteristic curve consists of three distinct regions:
1. The forward-bias region, determined by v > 0
2. The reverse-bias region, determined by v < 0
3. The breakdown region, determined by v < -VBR
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The Forward-Bias Region
𝑖 = 𝐼𝑠 (𝑒 𝑣/𝑉𝑇 − 1)
𝑉𝑇 =
𝑘𝑇
= 0.0862𝑇 (𝑚𝑉)
𝑞
where k = Boltzmann’s constant = 8.62 x 10-5 eV/K = 1.38 x 10-23 joules/kelvin
T = the absolute temperature in kelvins = 273 + temperature in °C
q = the magnitude of electronic charge = 1.60 x 10-19 coulomb
VT is 25.3 mV at 20oC
A good approximation:
𝑖 = 𝐼𝑠 𝑒 𝑣/𝑉𝑇
𝑖
𝑣 = 𝑉𝑇 𝑙𝑛
𝐼𝑆
What is k, T and q?
IS is a constant for a given diode as a given temperature
For high carrier injection:
𝑖 = 𝐼𝑠 (𝑒 𝑣/𝑛𝑉𝑇 − 1)
where n is from 1 to 2.
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The Reverse-Bias Region
𝑖 ≈ −𝐼𝑆
Real diodes exhibit reverse current much larger than IS. A small-signal diode whose IS is on the order of 10-14 A to 10-15 A
could show a reverse current on the order of 1 nA.
IS doubles for every 5oC rise in temperature.
Reverse current is mostly due to leakage effects. It doubles for every 10oC rise in temperature.
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The Breakdown Region
• Beyond the breakdown voltage VBR ~ zener breakdown at the “knee” of i-v curve
Normally not destructive
Used in voltage regulator
∆V = 𝑟𝑧 ∆𝐼
rz is the incremental resistance or dynamic resistance of Zener diode
• VZ = VZ0 + rZ IZ
• For IZ > IZK and VZ > VZ0
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Power supply
𝑁2
𝑣𝑠 = 𝑎𝑐 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑜𝑓 230
𝑁1
230 Vrms
50Hz
Power transformer
Ripple  dc output
dc Power supply
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The Half-Wave Rectifier
𝑣𝑠 = 𝑉𝑠 𝑠𝑖𝑛𝜃, 𝜃 = 2𝜋𝑓𝑡
1. Current-handling capability required of the diode;
2. Peak inverse voltage (PIV) that the diode must be
able to withstand without breakdown
𝑣𝑜 = 0 ;
𝑣𝑠 < 𝑉𝐷
𝑣𝑜 = 𝑣𝑠 − 𝑉𝐷 ;
𝑣𝑠 < 𝑉𝐷
PIV = VS
(Considering reverse bias) 16
The Rectifier with a Filter Capacitor – The peak Rectifier
Average of vo is
1
𝑉𝑜 = 𝑉𝑝 − 𝑉𝑟
2
𝑣𝑜 = 𝑉𝑝 𝑒 −𝑡 𝐶𝑅
At the end of discharge interval
𝑉𝑝 − 𝑉𝑟 ≈ 𝑉𝑝 𝑒 −𝑇 𝐶𝑅
(use Taylor expansion)
𝑉𝑟 ≈ 𝑉𝑝 𝑇/𝐶𝑅
𝑉𝑝
𝑉𝑟 ≈
𝑓𝐶𝑅
𝐼𝐿
𝑉𝑟 ≈
𝑓𝐶
𝑖𝐷𝑎𝑣 = 𝐼𝐿 (1 + 𝜋 2𝑉𝑝 𝑉𝑟 )
𝑖𝐷𝑚𝑎𝑥 = 𝐼𝐿 1 + 2𝜋 2𝑉𝑝 𝑉𝑟
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The Rectifier with a Filter Capacitor – The peak Rectifier
• For a full-wave rectifier circuit with a capacitor, discharge period T is replaced by T/2 :
𝑉𝑟 ≈
𝑉𝑝
2𝑓𝐶𝑅
≈
𝐼𝐿
2𝑓𝐶
𝑖𝐷𝑎𝑣 = 𝐼𝐿 1 + 𝜋 𝑉𝑝 2𝑉𝑟
𝑖𝐷𝑚𝑎𝑥 = 𝐼𝐿 1 + 2𝜋 𝑉𝑝 2𝑉𝑟
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