Among the greatest challenges in designing today's power-consumingproducts is managing the system's thermal budget. Since most electronicequipment include some form of power conversion, it is necessary tounderstand the design's thermal constraints, which form the context formany design decisions.
In most power-conversion circuits, the hottest elements are thepower ICs – diodes, MOSFETs and IGBTs. For a given circuit topology,these components heat up as functions of applied voltage, load current,switching frequency, gate-drive circuit, package type and mounting.
Of these, the first four dissipate power and model as thermalsources, while the last two models as thermal sinks because they removeheat from the system.
A good first-order estimate of power dissipation in switchmodecircuits is P = DVI, where I is the average conduction-cycle currentthrough the power IC, V is the average conduction-cycle voltage acrossthe device, and D is the duty cycle.
|Figure1: The power IC's datasheet provides thermal response curves, fromwhich you can calculate the device's temperature rise above the casetemperature when operating in switched-mode.|
In physical circuits, current is a function of circuit operation.Voltage is a function of current, the device type, junction temperatureand IC control method. For example, the forward voltage across a diodeis simply a function of current and temperature.
The voltage across a MOSFET in the on state is IDRDS(on) – theproduct of drain current and channel resistance. RDS(on), in turn, is afunction of ID, gate drive and temperature. The voltage across an IGBTin the on state, V=VCE(sat), is a function of current, gate drive andtemperature.
To determine the IC's temperature rise, multiply the powerdissipation by the thermal impedance. The limitation with this analysisis that it oversimplifies the power calculation and does not accountfor transient conditions.
The power device's data sheet provides thermal response curves,however, with which you can overcome that limitation (Figure 1 above ).
The curves assume a rectangular power pulse of amplitude P forduration t with duty cycle D. Follow the curve appropriate to yourcircuit's duty cycle to the point along the horizontal axiscorresponding to the pulse duration. Read the corresponding thermalresponse from the vertical axis and multiply that value by the powerdissipation to arrive at the temperature rise from case to junction.
|Figure2: The power IC's thermal stack includes the junction, substrate, case,thermal paste or other thermal interface material, heat sink, andambient.|
The thermal response curves only address the case-to-junctiontemperature rise. They cannot account for the case's mounting method,which contributes to its rise above ambient as a complete thermal-stackmodel indicates (Figure 2 above ).
Rather than approach the problem piece-by-piece, using differenttools and data sources to solve each part of the problem, a circuitsimulator can calculate the total thermal response. The simulator alsoallows you to observe the effect of the thermal system on the circuit'sparametric performance, which is difficult to deduce from pen-and-paperor spreadsheet analyses.
Circuit simulation uses component models and network analysis, whichclosely approximates the operating conditions for each device in thecircuit. The simulator automatically calculates the power dissipationof power devices, taking into account a full range of circuit anddevice behaviors that include gate drive, switching transitions anddiode reverse-recovery.
|Figure3: A quasidynamic thermal wrapper model accounts for the power device'sparametric dependence on temperature.|
However, traditional circuit simulators calculate power based on astatic thermal model. In other words, they fix device behavior withrespect to temperature. This is adequate for low-power IC simulationbecause devices in such circuits exhibit little self-heating.
Power ICs do self-heat, however, and an accurate simulation mustaccount for the device behavior's temperature dependence. Adding aquasidynamic thermal wrapper model to the static 25 degrees C devicemodel overcomes this limitation (Figure3 above ).SPICE can implement the thermalwrapper in macro models. Popular non-SPICE simulators can alsoimplement the thermal wrapper with macro models.
Alternatively, they can implement the thermal wrapper in a hardwaredescription language such as VHDL-AMS for Ansoft's Simplorer, MAST for Synopsys's Saber, or Verilog for Cadence's Spector simulators.Because all of these simulators can use macro models, this articlefocuses on that approach and models a power MOSFET as an example.
The thermal wrapper must implement two temperature dependent MOSFETparameters: the threshold voltage, Vth, and the fully enhanced channelresistance, RDS(on). The temperature coefficient of Vth isapproximately -7mV/°C. RDS(on)'s temperature-dependence modelsreasonably well with a quadratic. Implementing the mathematicalrelationships is easy – deriving the operating temperature that drivesthese functions is the challenge.
The thermal system usually models as a ladder network comprising Rsand Cs with a step response resembling the single pulse curve in Figure 1 previously. Most newMOSFET datasheets include the ladder network, but older datasheets onlyprovide the curves. In this ladder model, power is analogous to currentand temperature is analogous to voltage.
|Figure4: The simulator's calculation of instantaneous power appears as acurrent source to the thermal network.|
The first item to obtain for the thermal-wrapper model is channelresistance as a function of temperature, RDS(on)(Tj), which all MOSFETdatasheets provide in the form of a characteristic curve. A simplequadratic curve- fitting routine can provide the three coefficients inthe form the model requires: RDS(on)(Tj) = RDS(on)(25 degrees C)(aTj2 +bTj +c).
The simulator computes the value of RDS(on)(25 degrees C) from thedevice's Spice model. Taking the derivative of the channel resistancewith respect to temperature yields an expression for the self-heatingeffect on RDS(on): dRDS(on)(Tj) = RDS(on)(25 degrees C)(2aTj +b)dTj.Add dRDS(on) as a resistor in series with the MOSFET's drain.
The next step calculates Tj from the MOSFET's instantaneous power.Neglecting switching losses in RG, the gate-interconnect resistance,this is simply: p = iDvDS. This power term serves as the source to thethermal ladder network (Figure 4 above ).
Note that the absolute-value block in Figure 4 is necessary becausepower dissipation always adds heat to the system, no matter what thesign of the voltage or current. The output of this model is a voltagethat corresponds to Tj.
Finally, the shift in Vth compared with the nominal 25 degrees Cthreshold is simply:
This term appears as a floating voltage source in series with theMOSFET's gate terminal. With the characterizing equations in hand,creating the model is straightforward. Obtain from its manufacturer theMOSFET's datasheet, Spice model and thermal network. Newer MOSFETdatasheets include the thermal networks.
|Figure5: The complete quasidynamic thermal simulation model provides insightsthat fixed-temperature simulations and hand thermal analyses cannot.|
Obtain or calculate the quadratic coefficients that describeRDS(on)'s temperature coefficient. Finally, implement the macro model,including the equations for dRDS(on)(Tj), the absolute value of theinstantaneous power and dVth(Tj) (Figure5 above ).
The if-else statements in Figure 5 account for the MOSFET's stateduring simulation. If VDS is greater than 100mV, a 1 micro-ohmresistance adds to the channel.
The model assumes that the MOSFET is fully on if VDS is less than100mV and it adds the temperature dependent dRDS(on). In this simplemodel, Ta is the case temperature. It's easy to expand the thermalnetwork, however, to include a heat sink's performance and its effecton the system.
David Divins is Senior Applications Engineer, International Rectifier.