ECE1750, Spring 2018 Week 1 - Components 1
Most commonly used power electronic switches: Diodes(aka (a.k.a. rectifiers) Thyristors (a.k.a. silicon controlled rectifiers, SCRs) Power MOSFETs IGBTs 2
But first, wires An ideal conductor has no impedance. A real conductor has a resistance. R l A Area A I Amps Current flowing through a resistance generate heat. This heat needs to be dissipated or the wire temperature will increase to the point when the wire will melt or the insulation around the conductor will be damaged. What are the current limits (ampacity)? 3
Wires The power dissipated per unit of volume in a wire is: 2 2 2 P I R I l I V la la A A 2 Since current density, J, equals current, I, divided by the cross sectional area A,then P V J Depending on the type of insulator used for the wires and how the cable is laid out (how tightly, whether it is in an enclosed environment with little air flow or not, etc.) copper cables can handle current densities up to 1000 A/cm 2 2 Area A I Amps Rated J usually about 100-200 Amperes/cm 2 4
Wires Due to skin effect (non-uniform current density distribution) ib ti )the resistance of a wire increases when the current frequency increases Resistance also changes with temperature (usually increases with temperature). This effect may not be noticeable for some conducting materials at normal operating temperatures. Other characteristics of wires: Self-inductance Capacitance with respect to other conductors 5
Wires Slfi Self-inductance of a wire of length l and conductor radius of R: 0 D r 0 0 D Lw ln l ln l 1/4 2 R 4 2 2 e R External Internal (about 0.5 nh/cm for Al and Cu) where D is the distance to a return conductor. So a single wire can be represented as It is also possible to observe that there is a capacitance between two wires separated by a distance d: 1 1 Cab Can Cbn l 2 2 ln d R d 6
Capacitors Capacitors store energy e in its electric ec c field. In ideal capacitors, the magnitude that relates the charge generating the electric field and the voltage difference between two opposing metallic plates with an area A and at a distance d, is the capacitance: q C A V In ideal capacitors: C d d Equivalent model of real standard capacitors: R l A A Leakage current Connecting wires A C d d Equivalent Series Resistance (ESR): ESR R w 1 R C 2 2 l
Impedance behavior of a real capacitor: Capacitors ESR Resonant frequency (XC = XL) Resistive behavior Capacitive Inductive Dissipation factor: R 1 1 tan ( ESR ) C X RC l Hence, the dissipation factor depends only on the materials property of the dielectric. 8
Capacitors Real capacitors dissipate i some heat given by P ( ESR) I In general the maximum power per unit of volume that capacitors can dissipate is about 0.1 W/cm 3. In some applications this is a limiting design factor (i.e., capacitors may not be big enough to dissipate all the power being dissipated due to a current flowing through the ESR. 2 Quality factor of a capacitor: Q L C ESR Lower Q Higher Q
Capacitors State variable: voltage Fundamental circuit equation: dv C ic C dt The capacitance gives an indication of electric inertia. Compare the above equation with Newton s F dv m dt Capacitors tend to hold their voltage fixed. For a finite current with an infinite capacitance, the voltage must be constant. Hence, capacitors tend to behave like voltage sources (the larger the capacitance, the closer they resemble a voltage source) The energy stored in a capacitor is WC 1 2 Cv 2
Capacitors Linear, but frequency dependent Resists sudden voltage changes with i = C dv/dt Impedance decreases with frequency Stored energy is proportional to squared voltage i leads v Distortion in voltage Voltage Current 11
Magnetic circuits N i Inductors μ l Φ A Permeability (μ = μrμ0) In vacuum μ0 =4π 10-7 H/m Magnetic flux (SI unit is Webers, Wb) Based on Ampere s law: Ni Hl where H is the magnetic field intensity (units of A/m). 12
Magnetic circuits Inductors The magnetic flux is HA where μ is the permeability of the magnetic core material and μh equals B, the magnetic flux density (units of Tesla). Assume by now that μ is constant so B and H are proportional (we will see later that μ is not always constant). So, NI l A where the magnetomotive force (mmf) is defined as NI and the reluctance is defined as l A 13
Magnetic circuits Inductors Analogies between electric and magnetic circuits Electric circuits it Magnetic circuits it Current i Magnetic flux mmf Electromotive force NI l l Resistance R Reluctance A A Ohm s law Ri Ampere s law Electric circuit Magnetic circuit Ri kk kk i j 0 j 0 14
Magnetic circuits Inductors Solving magnetic circuits with electrical circuits: i N μc μ μ0 lc A la c a lc A c la A 0 Air gap? Ni c a a c a Because μc>>μ0 15
Magnetic circuits Inductors Solving magnetic circuits with electrical circuits: l2 2 μ μc 1 3 l3 1 l 1 A c 1 2 A2 i N A1 l1 3 A3 2 l 2 c A 2 l 3 3 c A 3 2 2 1 2 3 1 3 1 3 Ni 113 3 Ni Ni 1 1 2 2 16
Inductance Inductors Let s define linkage flux as N According to Faraday s law: Then, d di v di dt v d dt Let s define inductance (units of Henry, H) as L d di 17
Inductance Since Then, L v d di di L dt Inductors if μ is constant, then 2 2 2 N N i N N A L i i i l Volumetric energy stored in an inductor: If μ is constant the energy stored in an inductor is w WL 11 B 2 1 2 2 Li 2 18
Magnetic materials Inductors In real magnetic cores μ is constant only for values of the mmf below a given limit. In reality, magnetic materials used for inductor cores have the following relationship between B and H Bsat 0.3T for Ferrite Bsat Bsat 1T to 2 T for powdered iron Remember that B Linear relationship: μ is constant Saturation: very small dλ/di Remember thatt i H 19
Magnetic materials Inductors When a magnetic core reaches saturation dλ/di is very small (or di/dλ is very large). Hence, from v d di di dt di di v dt d In saturation the current increases rapidly so after a short time of applying a relatively small voltage to a coil, the current increases to levels that causes the wire of an inductor winding to become excessively hot (because the wire has a resistance and i 2 R becomes too high). To avoid saturation: Ni B A sat sat 20
Magnetic materials Inductors Since 2 Ni B A N sat L the Ampere-turn limit is defined as Ni max Bsat l Bsat i A Usually specified in datasheets from a perunit inductance AL defined as 1 Lmax AL 2 N so i Volt-second rating max Bsat A NA L Also, v d N NBA vdt dt so vdt B NA B sat For dc voltages: Vdct Bsat NA For ac voltages: V peak N B sat A (max volt-sec @dc) (max volt/turn @ac) 21
Additional design notions Inductors Fill factor is the % of a core window that can be filled with the winding wire: ff 50% for EI, I, and pot cores ff = 10% for toroidal core Since And NA A ff max cond wind cond Window of a toroidal core Ni NI NA J Window of an EI core Then, J Ni max (usually, J is selected not exceeding 300 A/cm 2 ) A wind ff 22
Losses in inductors Inductors There are two components: Eddy currents and hysteresis Eddy currents (depends on the magnetic material used in the core and its resistivity) The varying magnetic flux induce currents that cause ohmic losses () t 23
Losses in inductors There are two components: Inductors Hysteresis: in order to change the polarization direction of the dipoles in the magnetic core it is necessary to provide energy to the core as part of an irreversible process. d di didt vdidt dt i( T) tt tt i(0) t 0 t 0 Area under magnetizing curve power energy The area of the hysteresis cycle (marked in red) is the energy lost in the irreversible process of reorienting magnetic dipoles in the magnetic core General formula to calculate losses found in datasheets: P / vol P f B loss o a b 24
Inductors Basic concepts Inductors are dual components of capacitors state variable: current Fundamental circuit equation: v L dil L dt The inductance gives an indication of electric inertia. Inductors will tend to hold its current fixed. Any attempt to change the current in an inductor will be answered with an opposing voltage by the inductor. If the current tends to drop, the voltage generated will tend to act as an electromotive force. If the current tends to increase, the voltage across the inductor will drop, like a resistance. For a finite voltage with an infinite inductance, the current must be constant. Hence, inductors tend to behave like current sources (the larger the inductance, the closer they resemble a current source) An inductor s energy is 2 W L 1 2 Li
Inductors Linear (with the indicated precautions and within an specified frequency range) Resists sudden current changes with v = L di/dt Impedance increases with frequency Stored energy is proportional to squared current i lags v Voltage Current 26
Power electronic switches Main characteristics ti of ideal switches No voltage drop when conducting current No current when it is open. Instantaneous transitions from conducting to open state and vice-versa. (Last characteristics imply that they do not dissipate power). (The characteristics of instantaneous transitions imply that it can operate switching on and off at any frequency, although, in reality, power electronic switches can operate up to a few khz to a few MHz depending on the type of switch used). Ideal switches can block voltages and conduct currents in both directions. Switches can be freely controlled to switch on or off. Switches will not turn on or off unless commanded to do so. 27
Power electronic switches Main characteristics ti of real switches There is a small voltage drop when conducting current There is some leakage current when it is open open. Real Switches can operate up to a given frequency depending on how fast internal capacitances can be charged or discharged. Hence, transitions from open to close and vice-versa versa are not instantaneous. (Last characteristics imply that real switches dissipate power when conducting and when commutating. Real switches can may only block voltages or conduct currents in one directions. It may not always be possible to freely controlled real switches from on or off so real switches may turn on or off even when not commanded d to do so. The main parameters characterizing power electronic switches are the conduction current (current when they are conducting) and the blocking voltage (the maximum voltage they can withstand t without t conducting current when they are commanded to be in the OFF state). 28
Power electronic switches First a word about BJT (bipolar junction transistors) t applied to power electronic circuits BJTs were used for many years but nowadays the most commonly used transistors as power electronic switches are MOSFETs and IGBTs. Issues with BJTs: Current controlled Efficiencyi Reliability 29
Diodes i Power Schottky + v Zener Anode Cathode Switching Reverse breakdown i v Controllability? - Uncontrolled turn on, uncontrolled turn off. Vj, about 0.8 1.2V Typical power diodes static characteristic Built-in potential 30
Diodes Main characteristics (PIN diodes) Diodes conduct when a forward biased voltage greater than the built-in potential is applied to its terminal. Diodes stop conducting when they are not forward biased and the current reaches 0 A. If a reversed biased voltage greater than the reverse breakdown voltage is applied to a diode, then the diode will conduct a negative current but it will be the first and last time the diode will conduct in such conditions. When conducting power diodes show a voltage drop between 0.8 V to 1.2 V or more. 31
Diodes Main characteristics (PIN diodes) Traditional diode Power diodes (PIN diodes) p-type p-type n-type intrinsic n-type p-type semiconductors contain an excess of holes. n-type semiconductors contain an excess of electrons. The intrinsic layer is not doped in any way (no excess of charges). The wider the intrinsic layer is, the larger the breakdown voltage is, but the larger the capacitance between anode and cathode is, resulting in a slower switching action. Typical power diodes are made of silicon (Si). New materials include SiC and GaN. 32
Diodes Main characteristics (PIN diodes) Diode static model: ON OFF RON Vj Diode dynamic model + VD - Diffusion capacitance: increases with wider intrinsic region LW R(sw) V(sw) R(sw) = RON ROFF if sw = 1 (RON in the order of mohms) if sw = 0 (ROFF in the order of MOhms) 33
Diodes Main characteristics (PIN diodes) Note: scales have been exaggerated to show diode behavior clearer. ION vd id Diode turn-on Diode ON Vj Diode turn-off Reverse recovery charge Diode OFF t t Reverse recovery current : charge buildup in the diffusion capacitance flows out of the junction VOFF During turn-on and turn-off the diffusion capacitance is charged or discharged, respectively. Hence, turn-on and turn-off are not instantaneous processes. 34
Thyristors (a.k.a. silicon controlled rectifiers, SCRs) i Gate + v Anode Cathode When forward biased, it becomes a diode when a pulse of gate current is injected ( firing the gate ) Then, like a diode, it turns off when the current tries to reverse. Controllability: controlled turn on but uncontrolled turn off 35
Thyristors Equivalent physical configuration of thyristors: A positive feedback loop makes it to keep conducting after the current pulse at the gate is removed. 36
Thyristors i G A + vak K Thyristor static behavior. Note: scales in the next figure have been exaggerated i Reverse breakdown Reverse leakage current ig,1 > ig,2 > ig,3 ig,1 voltage IL ig,2 ig,3 IH I vak Forward leakage current Forward breakdown voltage 37
Thyristors Normally, thyristors are switched on when they are forward biased and a pulse of current (usually a few ma) is applied to the gate at least until the cathode current exceeds the latching current (usually the current pulse duration is about a few micro-seconds. The thyristors cannot be turned off until the cathode current falls at least below the latching current. Other ways of turning on a thyristor considering it is forward biased: Apply an anode-cathode voltage at least equal to the forward breakdown voltage. Apply a large dvak/dt so a current pulse originates due to parasitic capacitances. Higher temperatures Failure modes: di/dt (related to uneven distribution ib ti of the initial iti current and 2 nd rupture). breakdown voltages (both forward and inverse biased). 38
Power MOSFETs (a high-speed, voltage-controlled switch) D: Drain D If desired, a series blocking diode can be inserted here to prevent reverse current G: Gate G S: Source Switch closes when V GS 4Vdc S N channel MOSFET equivalent circuit Controllability? - Controlled turn on, controlled turn off (but there is an internal antiparallel diode). Thanks to the diode it can conduct in both directions but it cannot block D-S voltages in which VD<VS. Controlled through the gate by voltage. If VGS>VGS,th it conducts. Otherwise, it does not conduct (in the forward direction). 39
Power MOSFETS Main characteristics MOSFET = Metal oxide field effect transistor. A channel is established in order to conduct charges. Examples of n- channel MOSFETs Lateral MOSFET V-MOS The thin Aluminum-Oxide is very sensitive to electrostatic electricity. MOSFETs are protected by placing a large (e.g. 100 kohm resistor between Gate and Source). Additionally, current into the gate is limited by placing a gate resistor (usually ~10 ohm) and a small ferrite core that limits di/dt into the gate. Snubers are used to protect MOSFETs for 2 nd rupture observed particularly with inductive loads. 40
Main characteristics Static Characteristic Power MOSFETS Ohmic Region ON State Active Region i id id ON State Higher VGS Lower Cutoff (OFF State) VGS<VGS,th v vds VGS,th VDS vgs 41
Power MOSFETS Main characteristics Behavioral models Static model (sw) sw = ON when V VGS>VGS,th OFF when VGS<VGS,th Dynamic Model G C Cgd Cgs id Capacitances (particularly D Cgs) ) need to be charged or rd(t) discharged to turn the MOSFET ON or OFF, respectively Cds RDS,ON S 42
Power MOSFETS Main characteristics Note: scales have been exaggerated to show the MOSFET behavior clearer. VGG OFF to ON VGG ON to OFF vgs VGS,th t Exponential curve: Cgs is being charged through RG t vgs t t id i id t t vds vds t t 43
Main characteristics IGBTs IGBT = Isolated gate bipolar transistor. It is like a BJT but turn-on and turn off is controlled by voltage. I.e., it conducts when the base to emitter voltage is higher than a threshold. A negative voltage between base and emitter needs to be applied to turn-off the IGBT. IGBTs have controlled turn-on and turn-off and conduct in only one direction. 44
Main characteristics Physical configuration IGBTs Equivalent dynamic behavioral model The conductance is a function of vgs: small conductance when OFF and large conductance when ON G(vGS) =1/RC ic rc Non-linear capacitance VSS C(q) VSS is constant 45
Summary Main characteristics of various power electronic switches technologies Figure from Prof. Mohan s book 46