電子回路論第 7 回 Electric Circuits for Physicists #7
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1 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
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 10k Combination of op-amp and discrete transistors 10m a a 10m Complementary push-pull V + R i R f 10k v in R in - R f + v out v in R in J in = J v out Inversion amplifier V R i Voltage, current booster
4 pn-junction in reverse bias region V bi + V Built-in potential Depletion layer Poisson equation p w p w n n Space charge density: Boundary condition: Solution:
5 Varicap diode Reverse bias voltage widens depletion layer. V bi V Varicap diode KB505 Frequency modulation (FM), Phase lock loop (PLL)
6 4.4 Field effect transistor (FET) D D Circuit symbols G G S n-channel S p-channel
7 Static characteristics of FET Ohmic area Space charge limited area
8 Space-charge limitation of source-drain current S n -N D e p+ L V ch (y) G w d (y) 2w t D Travel distance (y) dependent potential Depletion layer width p+ G V g y conductivity electric field channel width Approx. for w d < w t /2
9 Static characteristics of FET transconductance drain resistance Local linear approximation: Amplification factor (voltage gain)
10 Biasing circuits for FETs: Fixed bias circuit Local linear approximation action point (the center of parameters) The action point is determined by resistors and dc power sources. Biasing circuit V DD R D J D V DD V DS
11 Biasing circuits for FETs: Self-biasing circuit V DD R D + R S J D V GS V DD V DS
12 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
13 Voltage gain A V (db) Example of source-grounded FET amplifier R S is working as a negative feedback circuit. 120k 10k ignore r d 1m G D S 1m A V 40k 5k R + 10m f (Hz)
14 Simulation by LTSpice
15 Metal-Semiconductor (MES) FET Walter Schottky
16 Metal-Oxide-Semiconductor (MOS) FET enhancement depletion inversion
17 Complementary MOS logic gates Simplified CMOS inverter circuit Low leakage current FinFET structure Single gate input both on/off switch
18 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.
19 Summary of chapter 4 Amplification circuit Feedback (feedforward) Operational amplifier Transfer function diagram Stability criteria Elements for amplification (non-linear treatment. Bias circuits + signal circuits.) Bipolar transistors (Semiconductor physics) Field effect transistors OP amp selection BT input High precision Low voltage noise Large power output FET input Low bias current/ High input impedance Low power consumption
20 Ch.5 Distributed constant circuits Submarine cable map
21 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
22 5.1.1 Coaxial cable Thin coaxial cable AWG50 (f25mm)
23 Transmission line as a series of infinitesimal terminal-pairs Transmission line divide into four terminal circuits Each unit should have delay. Ignore energy dissipation. Oliver Heaviside L C L C L C L C L C L C J dx J + dj Then take the infinitesimal limit Zdx Width 0, Number V Ydx V + dv Z, Y : Impedance, Admittance per unit length
24 Characteristic impedance : telegraphic equation -: Progressive, +: Retrograde Impedance: Pure reactance Y = iωc, Z = iωl for L and C model (physical dimension: velocity) Characteristic impedance:
25 Maxwell theory for coaxial cable y a b a: inner metal radius, b: radius of outer cylinder, e: insulator dielectric constant, m: magnetic permeability From Maxwell equations z x In TEM (transverse electric and magnetic) mode: For the fields along x and y to survive, Propagation velocity
26 Maxwell theory for coaxial cable In TEM mode: potentials are available. That is is an analytic function of Cauchy-Riemann condition Characteristic impedance: : potential at a, b This expression represents the equivalence of distributed constant circuit model and the Maxwell theory for coaxial cable. Capacitance part
27 Maxwell theory for coaxial cable Inductance part Core current J, shield current J Flux per length: Self inductance per length: cf. Characteristic impedance of the vacuum
28 Coaxial cable 2
29 Coaxial connectors
30 Coaxial connectors
31 Coaxial connectors 2 SMA-type jack plug K-type V-type
32 LEMO cables and connectors High-energy physics experiment, etc.
33 Transmission lines with TEM mode Transmission lines with two conductors are families. Electromagnetic field confinement with parallel-plate capacitor Roll up to coaxial cable Open to micro-strip line Shrink to dipole (Lecher line) Commonly TEM is the primary mode.
34 Lecher line
35 Micro strip line Wide (W/h>3.3) strip Narrow (W/h<3.3) strip
36 Waveguide metal hollow cross section Electromagnetic field is confined into a simplyconnected space. Maxwell equations give TEM mode cannot exist. Helmholtz equation E z = 0: TE mode, H z = 0: TM mode
37 Optical fiber Difference in dielectric constant step-type optical fiber no dispersion
38 Connection and termination Z 0 Z 1 At x = 0: J = J + + J progressive retrograde (definition right positive) V = V + + V = Z 0 J + J -l 0 Termination of a transmission line with length l and characteristic impedance Z 0 at x = 0 with a resistor Z 1. Comment: Sign of Ohm s law in transmission lines reflects direction of waves (depends on the definitions). x Reflection coefficient is 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
39 Connection and termination Finite reflection Standing wave Voltage-Standing Wave Ratio (VSWR): 1 r 1 + r At x = l Then at x = l (at power source), the right hand side can be represented by Reflection coefficient:
40 SWR measurement SWR Meters: desktop types cross-meter handy type directional coupler
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