Vrej Barkhor oweMsegude.Ca Discrete power MOSFETs employ ser circuits,although the device geometry,voltage and current devices.The metal oxide semiconductor field effect p-Substrate tra he 70s.Figure 1 shows the device schematic,transfer (a) characterist of the MOSFET was partly driven by the limitations of bip olar power sistors(BJTs) device of choice in .er s the electronics applications. 0 (b) we will loosely refer to the fatealeiia0viR The bipola istor is large base dri as on keep the device in the ON ired to state. (c) Also.higher Figure 1.Power MOSFET(a)Schematic,(b)Transfer Characteristics,(c) curre Device Symbo fast turn-off.Despite the very advanced state of manufacturability and lower costs of BJTs,these aave made the base drive circuit design more complicated and hence more expensive than the
Power MOSFET Basics Vrej Barkhordarian, International Rectifier, El Segundo, Ca. Discrete power MOSFETs employ semiconductor processing techniques that are similar to those of today's VLSI circuits, although the device geometry, voltage and current levels are significantly different from the design used in VLSI devices. The metal oxide semiconductor field effect transistor (MOSFET) is based on the original field-effect transistor introduced in the 70s. Figure 1 shows the device schematic, transfer characteristics and device symbol for a MOSFET. The invention of the power MOSFET was partly driven by the limitations of bipolar power junction transistors (BJTs) which, until recently, was the device of choice in power electronics applications. Although it is not possible to define absolutely the operating boundaries of a power device, we will loosely refer to the power device as any device that can switch at least 1A. The bipolar power transistor is a current controlled device. A large base drive current as high as one-fifth of the collector current is required to keep the device in the ON state. Also, higher reverse base drive currents are required to obtain fast turn-off. Despite the very advanced state of manufacturability and lower costs of BJTs, these limitations have made the base drive circuit design more complicated and hence more expensive than the power MOSFET. Source Contact Field Oxide Gate Oxide Gate Metallization Drain Contact n* Drain p-Substrate Channel n* Source t ox l VGS VT 0 0 I D (a) (b) I D D SB (Channel or Substrate) S G (c) Figure 1. Power MOSFET (a) Schematic, (b) Transfer Characteristics, (c) Device Symbol
Another BIT limitation is that both electrons and holes contribute to conduction.Presence of holes with their higher 20001 carrier lifetime cau 150 the an Tepeo forward voltage drop decreases with increasing temperature 00( causing diversion of current to a single device when several 500 devices are paralleled.Power MOSFETs.on the other hand. MOS are 0 10 10 ing power losses are im ortant.Plus.they can withstand simultan f high current and voltage without e failure Figure ue to cond bi wn.Power Limitations of MOSFETs and BJTs. the voltage dron increases with increasing temperature ensu ing an even distribution of current among all components. on-state volt the powe er MOSFET becomes to use the bipolar power transistor at the exp nse of worse high fre e performance.Figure 2 shows the present current-voltage limitations of power MOSFETs and BJTs.Over time,new materials, structures and processing techniques are expected to raise these limits. Source p*Body Reglon Drift Region n'Epi Layer Drain Figure 3.Schematic Diagram for an n-Channel Power MOSFET and the Device
Another BJT limitation is that both electrons and holes contribute to conduction. Presence of holes with their higher carrier lifetime causes the switching speed to be several orders of magnitude slower than for a power MOSFET of similar size and voltage rating. Also, BJTs suffer from thermal runaway. Their forward voltage drop decreases with increasing temperature causing diversion of current to a single device when several devices are paralleled. Power MOSFETs, on the other hand, are majority carrier devices with no minority carrier injection. They are superior to the BJTs in high frequency applications where switching power losses are important. Plus, they can withstand simultaneous application of high current and voltage without undergoing destructive failure due to second breakdown. Power MOSFETs can also be paralleled easily because the forward voltage drop increases with increasing temperature, ensuring an even distribution of current among all components. However, at high breakdown voltages (>200V) the on-state voltage drop of the power MOSFET becomes higher than that of a similar size bipolar device with similar voltage rating. This makes it more attractive to use the bipolar power transistor at the expense of worse high frequency performance. Figure 2 shows the present current-voltage limitations of power MOSFETs and BJTs. Over time, new materials, structures and processing techniques are expected to raise these limits. 2000 1500 1000 500 0 1 10 100 1000 Maximum Current (A) Holdoff Voltage (V) Bipolar Transistors MOS Figure 2. Current-Voltage Limitations of MOSFETs and BJTs. Drain Metallization Drain n+ Substrate (100) n- Epi Layer Channels n+ n p + p+ Body Region p+ Drift Region G S D Source Gate Oxide Polysilicon Gate Source Metallization Figure 3. Schematic Diagram for an n-Channel Power MOSFET and the Device
Figure 3 shows schematic diagram and figure 4 shows the physical origin of the parasitic components in an n-channel power MOSFET.The parasitic JFET appearing between the two body implants restricts current flow when the depletion wid acent body diodes extend into the drift region with ain vol ge.T RB must b levice sus sced thr thon-on doping and distance under the source region.There are several parasitic capacitances associated with the power MOSFET as shown in Figure 3. Ccs is the capacitance due to the overlap of the source and the channel regions by the polysilicon gate and is independent of applied voltage.CcD consists of two parts.the first is the capacitance associated with the overlap of the polysilicon gate and the silicon underneath in the JFET region.The second part is the capacitance associated with the depletion region immediately under the gate.CcD is a nonlinear function of voltage.Finally,Cps,the capacitance associated with the body-drift diode,varies inversely with the square root of the drain-source bias.There are currently two designs of power MOSFETs,usually to as the pla r and the trench designs. The plan ign has already been introduced in the technology has the ac ntage of higher cell density ore device. LTO gsm 本 CGS1 BJT Cos nEpi Layer n'Substrate Figure 4.Power MOSFET Parasitic Components
Figure 3 shows schematic diagram and Figure 4 shows the physical origin of the parasitic components in an n-channel power MOSFET. The parasitic JFET appearing between the two body implants restricts current flow when the depletion widths of the two adjacent body diodes extend into the drift region with increasing drain voltage. The parasitic BJT can make the device susceptible to unwanted device turn-on and premature breakdown. The base resistance RB must be minimized through careful design of the doping and distance under the source region. There are several parasitic capacitances associated with the power MOSFET as shown in Figure 3. CGS is the capacitance due to the overlap of the source and the channel regions by the polysilicon gate and is independent of applied voltage. CGD consists of two parts, the first is the capacitance associated with the overlap of the polysilicon gate and the silicon underneath in the JFET region. The second part is the capacitance associated with the depletion region immediately under the gate. CGD is a nonlinear function of voltage. Finally, CDS, the capacitance associated with the body-drift diode, varies inversely with the square root of the drain-source bias. There are currently two designs of power MOSFETs, usually referred to as the planar and the trench designs. The planar design has already been introduced in the schematic of Figure 3. Two variations of the trench power MOSFET are shown Figure 5. The trench technology has the advantage of higher cell density but is more difficult to manufacture than the planar device. Metal CGS2 Cgsm LTO CGD RCh CGS1 RB BJT n- p- CDS JFET REPI n- n- Epi Layer n- Substrate Figure 4. Power MOSFET Parasitic Components
BREAKDOWN VOLTAGE Breakdown voltage is the volt e at which the reverse-biased body-drift diode breaks dran the e characteristics of a Electron Flow edat 250uA drain current for drain voltages below BVpss and with no bias on the gate.no channel is the surface voltage is entirely rce supported by the rev ion.Tbody phenomena can occur in Oxide poorly designed and processed devices: rough and thoughiso8enench- n'Epl Layer Channel when the depletion source side nction ache source region at drain voltages below the rated avalan he voltage of the source and drain and uses a breakdown acter 7.Th WI. Figure 5.Trench MOSFET current flowing betwe source and drain is denoted by Ipss.There are tradeoffs to be made between Rpsion)that requires shorter channel lengths and punch-through avoidance that requires longer channel lengths. The reach-thr omenon occurs whe epletio th n region on the e drift side of the bo dy-drift p-n depletion edge enters the high carrier concentration substrate,a further increase in drain voltage will cause the electric field to quickly reach the critical value of 2x105 V/cm where avalanching begins
BREAKDOWN VOLTAGE Breakdown voltage, BVDSS, is the voltage at which the reverse-biased body-drift diode breaks down and significant current starts to flow between the source and drain by the avalanche multiplication process, while the gate and source are shorted together. Current-voltage characteristics of a power MOSFET are shown in Figure 6. BVDSS is normally measured at 250µA drain current. For drain voltages below BVDSS and with no bias on the gate, no channel is formed under the gate at the surface and the drain voltage is entirely supported by the reverse-biased body-drift p-n junction. Two related phenomena can occur in poorly designed and processed devices: punch-through and reach-through. Punchthrough is observed when the depletion region on the source side of the body-drift p-n junction reaches the source region at drain voltages below the rated avalanche voltage of the device. This provides a current path between source and drain and causes a soft breakdown characteristics as shown in Figure 7. The leakage current flowing between source and drain is denoted by IDSS. There are tradeoffs to be made between RDS(on) that requires shorter channel lengths and punch-through avoidance that requires longer channel lengths. The reach-through phenomenon occurs when the depletion region on the drift side of the body-drift p-n junction reaches the epilayer-substrate interface before avalanching takes place in the epi. Once the depletion edge enters the high carrier concentration substrate, a further increase in drain voltage will cause the electric field to quickly reach the critical value of 2x105 V/cm where avalanching begins. Source Gate Source Gate Oxide Channel Oxide n- Epi Layer n+ Substrate (100) Drain (b) S G S Electron Flow D (a) Figure 5. Trench MOSFET (a) Current Crowding in V-Groove Trench MOSFET, (b) Truncated V-Groove MOSFET
ON-RESISTANCE The on-state resistance of a power MOSFET is made up of several components as shown in Figure 8: RDS(on)=Rsource +Rch +RA +RJ+RD +Rsub +Rweml (1) where: Rsource=Source diffusion resistance Rch=Channel resistance RA=Accumulation resistance R="JFET"C eof the (J: Rp=Drift region resistance 20 Eaub Wafers with substrate resistivities of up to 20m0-cm are used for high voltage bigi0esethan5aacmoiow 15 Rwcml =Sum e,the 5 and drain Metallization and the silicon, metallization and Leadframe ggblenihehoteere Ios VS Vos LOCUS car Figure 9 shows the relative importance of age s gl oages the Rp 2 devices due to the higher resistivity or 1 lower background carrier concentration in 10 the epi.At lower voltages.the Rpstn is dominate d by the Drain Voltage (Volts) ce and tal t Fom th Figure 6.Current-Voltage Characteristics of Power MOSFET bond wires and leadframe.The substrate contribution becomes more significant for lower breakdown voltage devices. TRANSCONDUCTANCE Transconductance,gfs,is a measure of the sensitivity of drain cu rrent to char nge s in rce bias This n drain c ent equal to ne half of the maximum current rating value and for a VDS that ensures operation in the constant current region. Transconductance is influenced by gate width,which increases in proportion to the active area as cell density increases ensity ha s increased over the yearsfro und half on per square inch in 198 aroun gnt m ell dmar on Ior t ren siti and th allows contacts to e made to the source in the center of the cels
ON-RESISTANCE The on-state resistance of a power MOSFET is made up of several components as shown in Figure 8: (1) where: Rsource = Source diffusion resistance Rch = Channel resistance RA = Accumulation resistance RJ = "JFET" component-resistance of the region between the two body regions RD = Drift region resistance Rsub = Substrate resistance Wafers with substrate resistivities of up to 20mΩ-cm are used for high voltage devices and less than 5mΩ-cm for low voltage devices. Rwcml = Sum of Bond Wire resistance, the Contact resistance between the source and drain Metallization and the silicon, metallization and Leadframe contributions. These are normally negligible in high voltage devices but can become significant in low voltage devices. Figure 9 shows the relative importance of each of the components to RDS(on) over the voltage spectrum. As can be seen, at high voltages the RDS(on) is dominated by epi resistance and JFET component. This component is higher in high voltage devices due to the higher resistivity or lower background carrier concentration in the epi. At lower voltages, the RDS(on) is dominated by the channel resistance and the contributions from the metal to semiconductor contact, metallization, bond wires and leadframe. The substrate contribution becomes more significant for lower breakdown voltage devices. TRANSCONDUCTANCE Transconductance, gfs, is a measure of the sensitivity of drain current to changes in gate-source bias. This parameter is normally quoted for a Vgs that gives a drain current equal to about one half of the maximum current rating value and for a VDS that ensures operation in the constant current region. Transconductance is influenced by gate width, which increases in proportion to the active area as cell density increases. Cell density has increased over the years from around half a million per square inch in 1980 to around eight million for planar MOSFETs and around 12 million for the trench technology. The limiting factor for even higher cell densities is the photolithography process control and resolution that allows contacts to be made to the source metallization in the center of the cells. R R R R RR R R DS(on source ch A J D sub wcml ) = + + ++ + + Gate Voltage 7 6 5 4 I DS VS VDS LOCUS 3 2 1 0 5 10 15 0 5 10 15 20 25 (Saturation Linear Region Region) Normalized Drain Current Drain Voltage (Volts) Figure 6. Current-Voltage Characteristics of Power MOSFET
nductance Reduced th is beneficial to both gfs and on-resistance with punch-through as a tradeoff.The lower limit of this length is se by the ab ity to cont ffusion THRESHOLD VOLTAGE Threshold voltage.Vth.is defined as the minimum gate electrod under the as req pol Is ust ally measured 2-4V for high voltage devices with thicker ate ovides and Figure 7.Power MOSFET Breakdown 1-2V for lower voltage.logic-compatible devices with thinner gate oxides With power MOSFETs finding incre sing use in portable electronics and wireless munications where battery power is at a premium,the trend is toward lower values of RD s(on)and DIODE FORWARD VOLTAGE GATE 7777777777777> The diode e.V. ds the SOURCE / the body-drain diode at as value of source current.Figure 10 typical characteristic for RSOURCE RCH P-BASE to the higher contact resistance I and p-silicon low voltage devices(<100V)are common. POWER DISSIPATION N+SUBSTRATE The maximum allowable power dissipation that will raise the die mum 77777777777777777777777777777777777 DRAIN is held at give by Pd where: Figure 8.Origin of Intemnal Resistance in a Power MOSFET. Pd_Tjmax-25 RthJC E Tmax=Maximum allowable temperature of the p-n junction in the device (normally 1500C or 1750C)Rthc =Junction-to-case thermal impedance of the device. DYNAMIC CHARACTERISTICS
Channel length also affects transconductance. Reduced channel length is beneficial to both gfs and on-resistance, with punch-through as a tradeoff. The lower limit of this length is set by the ability to control the double-diffusion process and is around 1-2mm today. Finally the lower the gate oxide thickness the higher gfs. THRESHOLD VOLTAGE Threshold voltage, Vth, is defined as the minimum gate electrode bias required to strongly invert the surface under the poly and form a conducting channel between the source and the drain regions. Vth is usually measured at a drain-source current of 250µA. Common values are 2-4V for high voltage devices with thicker gate oxides, and 1-2V for lower voltage, logic-compatible devices with thinner gate oxides. With power MOSFETs finding increasing use in portable electronics and wireless communications where battery power is at a premium, the trend is toward lower values of RDS(on) and Vth. DIODE FORWARD VOLTAGE The diode forward voltage, VF, is the guaranteed maximum forward drop of the body-drain diode at a specified value of source current. Figure 10 shows a typical I-V characteristics for this diode at two temperatures. Pchannel devices have a higher VF due to the higher contact resistance between metal and p-silicon compared with n-type silicon. Maximum values of 1.6V for high voltage devices (>100V) and 1.0V for low voltage devices (<100V) are common. POWER DISSIPATION The maximum allowable power dissipation that will raise the die temperature to the maximum allowable when the case temperature is held at 250C is important. It is give by Pd where: Tjmax = Maximum allowable temperature of the p-n junction in the device (normally 1500C or 1750C) RthJC = Junction-to-case thermal impedance of the device. DYNAMIC CHARACTERISTICS Sharp Soft I D BVDSS VDS Figure 7. Power MOSFET Breakdown Characteristics N+ R P-BASE SOURCE RCH RA RJ RD RSUB N+ SUBSTRATE SOURCE GATE DRAIN Figure 8. Origin of Internal Resistance in a Power MOSFET. Pd T j R thJC = max 25 - (2)
When the MOSFET is used as a switch,its basic function is to control the drain current by the gate Voltage Rating: 50V 100 500V ackaging lizatior Channol REPI Substrate Figure 9.Relative Contributions to Rpson)With Different Voltage Ratings The switching performance of a device is determined by the time required to establish voltage changes across of th cap. Ris the distributed resistan and is approximately invers RPortio activ area. nd LD are nductances and are around w tens of Typica npu reverse transfer C sheet capacitanc
When the MOSFET is used as a switch, its basic function is to control the drain current by the gate voltage. Figure 11(a) shows the transfer characteristics and Figure 11(b) is an equivalent circuit model often used for the analysis of MOSFET switching performance. The switching performance of a device is determined by the time required to establish voltage changes across capacitances. RG is the distributed resistance of the gate and is approximately inversely proportional to active area. LS and LD are source and drain lead inductances and are around a few tens of nH. Typical values of input (Ciss), output (Coss) and reverse transfer (Crss) capacitances given in the data sheets are used by circuit designers as a starting point in determining circuit component values. The data sheet capacitances are defined in terms of the equivalent circuit capacitances as: Voltage Rating: 50V 100V 500V Packaging Metallization Source Channel JFET Region Expitaxial Layer Substrate REPI RCH Rwcml Figure 9. Relative Contributions to RDS(on) With Different Voltage Ratings
Ciss=Cas+CGD.Cps shorted 100 Crss=CGD Coss CDS +CGD Gate-to-drain c most nonlinear function of voltage important parameter because it provides a T=150C feedback loop between the output and the 8中oea 25℃ than the sum of the static capacitances. Figure 12 shows a typical switching time test rcuit Vcs and Vps waveforms VGS=OV 0.5 1.0 15 20 25 Vsp Source-to-Drain Voltage (V) before drain current conduction can start. Figure 10.Typical Source-Drain (Body)Diode Forward Voltage Characteristics. Similarly.turn-off delay.td(om.is the time taken to discharge the capacitance after the after is switched off. Slope= 8 8 a
Ciss = CGS + CGD, CDS shorted Crss = CGD Coss = CDS + CGD Gate-to-drain capacitance, CGD, is a nonlinear function of voltage and is the most important parameter because it provides a feedback loop between the output and the input of the circuit. CGD is also called the Miller capacitance because it causes the total dynamic input capacitance to become greater than the sum of the static capacitances. Figure 12 shows a typical switching time test circuit. Also shown are the components of the rise and fall times with reference to the VGS and VDS waveforms. Turn-on delay, td(on), is the time taken to charge the input capacitance of the device before drain current conduction can start. Similarly, turn-off delay, td(off), is the time taken to discharge the capacitance after the after is switched off. 0.0 0.5 1.0 1.5 2.0 2.5 0.1 1 10 100 TJ = 1500C TJ = 250C VGS = 0V VSD, Source-to-Drain Voltage (V) ISD, Reverse Drain Current (A) Figure 10. Typical Source-Drain (Body) Diode Forward Voltage Characteristics. I D VGS Slope = gfs G RG CGD LD D D' S' CDS LS S CGS C I D Body-drain Diode (a) (b) Figure 11. Power MOSFET (a) Transfer characteristics, (b) Equivalent Circuit Showing Components That Have Greatest Effect on Switching
GATE CHARGE Rn Although input capacitance values are useful,they do not Vos provide accurate results when D.U.T. of devices G Effects of device size and transconductance n more useful parameter from the circuit design point of view is the gate charge rather than 10v clude both parameters on their data sheets. Figure 13 sho 可 wavefo d(on) tr GS Vcs starts to increas until it 100 eaches Vth. at which oint the drain current starts to flow and the Ccs starts to charge.During voltage continues to rise and drain current rises 901 is completely charged curre (b) Figure 12.Switching Time Test(a) Circuit,(b)VGS and VDS voltage starts to fall.With reference to the equivalent circuit model of the MOSFET shown in Figure 13,it can be seen that with Ccs fully charged at t2.VGs becomes constant and the drive current starts to charge the Miller capacitance,Cpc.This continues until time t3
GATE CHARGE Although input capacitance values are useful, they do not provide accurate results when comparing the switching performances of two devices from different manufacturers. Effects of device size and transconductance make such comparisons more difficult. A more useful parameter from the circuit design point of view is the gate charge rather than capacitance. Most manufacturers include both parameters on their data sheets. Figure 13 shows a typical gate charge waveform and the test circuit. When the gate is connected to the supply voltage, VGS starts to increase until it reaches Vth, at which point the drain current starts to flow and the CGS starts to charge. During the period t1 to t2, CGS continues to charge, the gate voltage continues to rise and drain current rises proportionally. At time t2, CGS is completely charged and the drain current reaches the predetermined current ID and stays constant while the drain voltage starts to fall. With reference to the equivalent circuit model of the MOSFET shown in Figure 13, it can be seen that with CGS fully charged at t2, VGS becomes constant and the drive current starts to charge the Miller capacitance, CDG. This continues until time t3. RD - + VDD VDS VGS RG D.U.T. -10V Pulse Width < 1µs Duty Factor < 0.1% (a) Figure 12. Switching Time Test (a) Circuit, (b) VGS and VDS Waveforms td(on) tr td(off) tf VGS 100% 90% VDS (b)
citance is VDD citan nce Ccs due to the rar pidly changi drain voltage i /dt). Once both of the capacita ces sand tc are fu The gate charg (Qo spo e t3 is the practice ① G dictates the use of a higher gate voltage rcthegba gate charge tions is Oc corresponding to t4. TEST CIR ge is that amount of current required from the drive switch the Time x current. example,a device with a gate charg e of can be turned on in 20usec if Ima is supplied to the gate or it can turn on in VOLTAGE G(TH have been possible with input capacitance values. DRAIN CURRENT dv/dt CAPABILITY Peak diode recove WAVEFORM rate is exceec tage acr s th Figure 13.Gate Ch (b)Resulting Gate forcing the device into current conduction mode,and r certain conditions a are two :LI vhich a dy/d e 14 sh may take pt model of ao of the gate-drain capacitance,CGD.When a voltage ramp appears across the drain and source terminal of the device a current Ii flows through the gate resistance,Rc.by means of the gate-drain capacitance. CcD.Rc is the total gate resistance in the circuit and the voltage drop across it is given by: VGS =IRG=RGCGD dt 3) When the gate voltage Vcs exceeds the threshold voltage of the device Vth.the device is forced into conduction.The dv/dt capability for this mechanism is thus set by:
Charge time for the Miller capacitance is larger than that for the gate to source capacitance CGS due to the rapidly changing drain voltage between t2 and t3 (current = C dv/dt). Once both of the capacitances CGS and CGD are fully charged, gate voltage (VGS) starts increasing again until it reaches the supply voltage at time t4. The gate charge (QGS + QGD) corresponding to time t3 is the bare minimum charge required to switch the device on. Good circuit design practice dictates the use of a higher gate voltage than the bare minimum required for switching and therefore the gate charge used in the calculations is QG corresponding to t4. The advantage of using gate charge is that the designer can easily calculate the amount of current required from the drive circuit to switch the device on in a desired length of time because Q = CV and I = C dv/dt, the Q = Time x current. For example, a device with a gate charge of 20nC can be turned on in 20µsec if 1ma is supplied to the gate or it can turn on in 20nsec if the gate current is increased to 1A. These simple calculations would not have been possible with input capacitance values. dv/dt CAPABILITY Peak diode recovery is defined as the maximum rate of rise of drain-source voltage allowed, i.e., dv/dt capability. If this rate is exceeded then the voltage across the gate-source terminals may become higher than the threshold voltage of the device, forcing the device into current conduction mode, and under certain conditions a catastrophic failure may occur. There are two possible mechanisms by which a dv/dt induced turn-on may take place. Figure 14 shows the equivalent circuit model of a power MOSFET, including the parasitic BJT. The first mechanism of dv/dt induced turn-on becomes active through the feedback action of the gate-drain capacitance, CGD. When a voltage ramp appears across the drain and source terminal of the device a current I1 flows through the gate resistance, RG, by means of the gate-drain capacitance, CGD. RG is the total gate resistance in the circuit and the voltage drop across it is given by: (3) When the gate voltage VGS exceeds the threshold voltage of the device Vth, the device is forced into conduction. The dv/dt capability for this mechanism is thus set by: VDD I D D D G S CGS CDG S I D TEST CIRCUIT (a) OGS OGD GATE VOLTAGE VG VG(TH) t 0 t 1 t 2 t 3 t 4 t DRAIN CURRENT DRAIN VOLTAGE VDD I D WAVEFORM (b) Figure 13. Gate Charge Test (a) Circuit, (b) Resulting Gate and Drain Waveforms. V IR R C dv dt GS G G GD = = 1