電子回路論第 7 回 Electric Circuits for Physicists
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1 電子回路論第 7 回 Electric Circuits for Physicists 東京大学理学部 理学系研究科物性研究所勝本信吾 Shingo Katsumoto
2 Outline 4.5 Field Effect Transistors (FETs) Ch.5 Distributed constant circuits 5.1 Transmission lines Coaxial cables Lecher lines Micro-strip lines 5.2 Wave propagation through transmission lines Connection and termination of transmission lines
3 Combination of an OP-amp and discrete transistors 10m 10k a Complementary push-pull V + R i R f 10k a 10m v in R in - R f + v out v in R in J in = J v out V R i Inversion amplifier Voltage, current booster
4 Depletion layer width with reverse bias voltage V bi + V Poisson equation p w p w n n
5 Effective capacitance and reverse bias voltage Doping profiler V bi V Varicap diode KB505 Frequency modulation Phase lock loop
6 4.4 Field effect transistor (FET) Junction FET (JFET) Circuit symbols D D G G S S n-channel p-channel Pinch-off
7 Static characteristics of FET Ohmic area Space charge limited area
8 Space-charge limitation of source-drain current L G p+ w d (y) S n -N D e p+ V ch (y) G 2w t V g D y conductivity electric field channel width pinch off (internal) voltage: Only valid for w d < w t /2.
9 Static characteristics of FET transconductance Low bias current: small power consumption Drain resistance Locally linear approximation Amplification factor (voltage gain)
10 Biasing circuits for FETs Fixed bias circuit R 1 R D V DD V DD J D J D R D V GS R 2 Self-biasing circuit V DD V DS Generally more stable R D V DD V DD R D + R S J D J D V GS R 2 V GS R S V GS V DD V DS
11 Equivalent signal circuits for FET G S D Source grounded Drain grounded Gate grounded v i - + μv i r d v i + - μv i 1 + μ r d 1 + μ v i - + μv i r d
12 MES-FET
13 MOS-FET enhancement Simplified CMOS inverter circuit depletion Low leakage current Single gate input both on/off switch inversion
14 MOSFET switching characteristics From datasheet CSD87381P power MOSFET (Texas instr.). More than 7 orders change in J D within 3 V change of V GS.
15 Ch.5 Distributed constant circuits Submarine cable map
16 Distributed constant circuit concept 1. In what case we need to consider distributed constant circuits? Characteristic sizes of devices wavelength of electromagnetic signal 2. A typical scheme to make the shift for distributed circuit Lumped constant circuit 1. Connection of unit circuits 2. Taking the infinitesimal limit Distributed constant circuit 3. Distributed constant circuits : transmission lines Coaxial cables, Lecher lines, micro-strip lines, waveguides, optical fibers
17 5.1.1 Coaxial cable Thin coaxial cable AWG50 (f25mm)
18 Transmission line as a series of infinitesimal terminal-pairs Transmission line divide into four terminal circuits Each unit should have delay. Ignore energy dissipation. L L L L L L C C C C C C Oliver Heaviside Then take the infinitesimal limit dx J J + dj Zdx Width 0, Number V Ydx V + dv Telegraphic equation
19 Characteristic impedance (dimension: L 1 ) -: Progressive, +: Retrograde Characteristic impedance Pure reactance Y = iωc, Z = iωl For L and C model (dimension: velocity)
20 Coaxial cable setup b r a e, m
21 Maxwell theory a b From Maxwell equations y z x However in TEM (transverse electric and magnetic) mode: i.e., the RHSs are zero. For the fields along x and y to survive, Propagation velocity In such a case, from Maxwell equations: Potentials are conceivable for H and E.
22 Maxwell theory Cauchy-Riemann theorem Characteristic impedance: If we can express V and J in the form of distributed constant circuit model (L and C model), the equivalence is certified. Capacitance part
23 Maxwell theory Inductance part Core current J, shield current J Flux per length: Self inductance per length: cf. Characteristic impedance of vacuum
24 Coaxial cable 2
25 Coaxial connectors
26 Coaxial connectors
27 Coaxial connectors 2 SMA-type jack plug K-type V-type
28 LEMO cables and connectors High-energy physics experiment, etc.
29 Lecher line
30 Micro strip line Wide (W/h>3.3) strip Narrow (W/h<3.3) strip
31 Connection and termination Z 0 Z 1 -l 0 x
32 Connection and termination J = J + + J (definition right positive) At x = 0: progressive retrograde V = V + + V = Z 0 J + J Reflection coefficient: Z 1 = Z 0 : no reflection, i.e., impedance matching Z 1 = + (open circuit end) : r = 1, i.e., free end Z 1 = 0 (short circuit end) : r = 1, i.e., fixed end
33 Connection and termination Finite reflection Standing wave Voltage-Standing Wave Ratio (VSWR): At x = - l Reflection coefficient:
34 SWR measurement SWR Meters: Desktop types Cross-meter Handy type
35 Connection and termination Z 0 Z 1 -l 0 x
36 Connection and termination Transmission line connection. Characteristic impedance Z 0, Z 0 At the connection point, only the local relation between V and J affects the reflection coefficient. The local impedance from the left hand side is Z 0.
電子回路論第 7 回 Electric Circuits for Physicists #7
電子回路論第 7 回 Electric Circuits for Physicists #7 東京大学理学部 理学系研究科物性研究所勝本信吾 Shingo Katsumoto Outline 4.5 Field Effect Transistors (FETs) Ch.5 Distributed constant circuits 5.1 Transmission lines 5.1.1 Coaxial
電子回路論第 6 回 Electric Circuits for Physicists
電子回路論第 6 回 Electric Circuits for Physicists 東京大学理学部 理学系研究科物性研究所勝本信吾 Shingo Katsumoto Outline 4.3 Feedback control 4.3.1 Disturbance and noise 4.3.2 PID control 4.4 PN junction transistors 4.4.1 Diodes
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