Electronic Circuits LaboratoryEE462GLab #5Dynamic Effects in P-N JunctionsInstrumentationThis lab requires the use of:¾ Oscilloscope, power supply, and function generator options.¾ The variable power supply to generate a DC offset in combination with a small AC component from the function generator (a potentially damaging situation for the equipment).Stored Energy and DynamicsThe output of a dynamic system depends on its previous excitation (input history) and the current input.¾ Previous excitation determines the stored energy in the energy storage elements (this information is sometimes given in terms of the initial conditions). ¾ The present input and the system state are required to determine the present output.¾ If energy storage or memory elements do not exist in a system, then the system is referred to as instantaneous, where the present output only depends on present input.Instantaneous Diode ModelPrevious labs have considered the diodes element as an instantaneous system completely described by the transfer characteristicForward BiasReverse BiasIdeal approximation:Short CircuitIdeal approximation:Open CircuitKneeVDIDVZIdAnode Cathode+ Vd- Anode Cathode+ Vd-Id0.7 VForward-Bias Practical ModelDynamic Diode ModelThe construction and layouts of circuits including connectors, devices, material interfaces, printed circuit boards, etc. result in capacitance / inductance. Since this is not intentionally designed into the the system it is sometimes referred to as parasitic or stray.The diode has 2 types of stray capacitance:¾ In reverse-bias mode depletion capacitance or junction capacitance exists.¾ In forward-bias mode diffusion capacitance exists.Reverse-Bias Junction CapacitanceThe PN junction accumulates charge from the minority carriers under reverse bias:Recall for parallel plate capacitors:A is the area of the junctionε is the dielectric constant+++++-----pn pn---------------+ + ++ + ++ + ++ + ++ + +d ddACε=Measuring Junction CapacitanceThe reverse biased voltage changes the effective capacitance of the diode, thus measurements must be made over a range of different reverse bias conditions.Since capacitance affects current flow relative to a CHANGING voltage (i =Cdv/dt), a small AC voltage excitation must be used in the neighborhood of each DC biasing voltage point to measure resulting AC currents and estimate capacitance as done in the first lab. The reverse bias diode capacitance can be characterized by a function of capacitance vs. reverse-bias voltage.Theoretical Behavior for Junction CapacitanceThe junction capacitance of a reversed biased diode is modeled by:¾ VRis the magnitude of the reverse-bias voltage¾ VJis the junction potential (Typical 1 volt)¾ m is the grading coefficient (Typical between .333 and .5)¾ CJOis the zero-biased junction capacitance.()mVVCVCJRJORJ⎟⎠⎞⎜⎝⎛+=1Derive an approximate expression relating Cjand VRon a log-log scale.Explain how m can be estimated from experimental measurements of Cjand VR.Test Circuit for Junction CapacitanceAnalyze the test circuit for measuring junction capacitance and find relationship between junction capacitance and junction voltage.1. Replace diode with a capacitor Cj.2. For superposition: deactivate VACand find Vd,, then deactivate VDC(apply arbitrary magnitude at 100kHz with zero phase for VAC).3. Apply superposition to find the resulting Vd.4. Find resulting Vdwith a nominal value for Cj= 23pF. VDC VAC VR+ -0.05µF1N4001100kΩRsense= 10kΩ Id+Vd-()°−+= 28k100299 .)(cos. tVVVACDCdπResult:Test Circuit for Junction CapacitanceFor the experiment VDCis used to set different operating points for the diode so the capacitance can be determined as a functionof reverse-bias voltage. VACmust be small in amplitude with a high frequency so as to move just the charge stored near the junction and not significantly change the reverse bias voltage. Id and Vdcan be measured with AC coupling for each VDC, and Cjestimated: VDC VAC VR+ -0.05µF1N4001100kΩ Rsense = 10kΩ +Vd-ωddjVICˆˆ=IdNote it is very important to have the .05µF capacitor in series with the function generator so as not to have DC current flowing into it and result in DAMAGE.Diffusion CapacitanceIn forward-bias mode holes are pushed to the n side and free electrons are pushed to the p side. Rapid switching to reverse bias results in minority carriers recombining and crossing the junction. This time tsis referred to as the storage interval. Then the depletion layer charges up. This time, tt, is referred to as the transition time. The total time is referred to as reverse recover time, trr.+-pn++++------+-pn++++------pn+++---V(IVM1)Time (s)TIME -1.000 V(3) -1.000 -1.000(V)0.0+10.0000.0 +10.000u +20.000u +30.000u +40.000utstttrrDiffusion CapacitanceThe diffusion capacitance is approximately, given by:¾τTis the transit time of minority carriers (typically varies from 10µs to 10ns)¾ IFis the forward quiescent current¾ VTis the thermal voltage equal to kT/qTFTdiffVIC)(τ=Diffusion CapacitanceThe total time (tsplus tt) is referred to as the reverse recovery time, trr. The energy storage interval tsis relate to the transit time of the minority carriers, given by:¾τTis the transit time of minority carriers (typically varies from 10µs to 10ns)¾ IFis the forward current before switching¾ IRis the reverse current after switching (during the storage interval)The transition time, tt, is determined by the effective RC (time constant of the circuit. (Note C is not constant over this interval)⎟⎟⎠⎞⎜⎜⎝⎛−−=RRFTsIIIt lnτDiffusion CapacitanceThe amount of charge stored is proportional to the forward current and the proportionality constant is called the transit time and has the units of seconds. In the last expression in above equation, IF is substituted out with the Shockley Equation:¾ Isis the saturation current (about 10-14A for small signal diodes at 300K)¾ q is the charge on an electron (1.6x10-19C)¾ T is the junction temperature in kelvins¾ k is Boltzmann's constant (1.38x10-23J/K)¾ n is a the emission coefficient (typically between 1 and 2)¾ VFis the voltage drop over the diode.⎟⎟⎠⎞⎜⎜⎝⎛−== 1nkTFqVsTFTeIIQττTest Circuit for Diffusion CapacitanceA square wave with a range of frequencies is used to observe the waveform of the current at the transition from on to off. Measure the reverse recovery time directly from the waveform and plot as a function of frequency. Rsense