What is DC biasing? If in terms of how a device is supplies with electricity, it is a method of providing a fixed value of either voltage or current.For instance, a power supply gives a constant value of voltage or current. A parametric analyzer sweep a value, and it is used to obtain the DC transfer function. Now, nothing prevent people using an SMU to bias a circuit (i.e.use it as power supply). If instead of sweeping a voltage (or current) have the SMU set to deliver a fixed value. A SMU provides a voltage and current,it is controlled in a way that you can sweep either. So SMU can be used as a DC supply or to characterize device in DC. From diodes prospective, biasing accounts for: Externally applying a diode a DC voltage source, which is presented by a battery, there will be a pn junction potential formed internally. Thus the current is conducted only in one direction, but blocked in the opposite direction. This is how forward-biased and reverse-biased de_ned.[11] From BJTs prospective, bias-ing means externally providing each terminal with a constant voltage value by externally connecting to a DC voltage source which can be batteries or DC power supplies. Because BJT has three terminals, its DC supply voltages are normally indicated as: VEE, VBB and VCC. ..Figure 8.1: A transistor is characterized by the relationships between currents and voltages at both input and output. The Input Characteristics is the IV characteristics curves that are measured at the emitter base junction.Iin = f(Vin). The Output Characteristics is the IV characteristic curves that are measured at the base collector junction.A SMU provides a voltage and current, it is controlled in a way that you can sweep between specified values. So it can be used as a DC supply or to characterize device in DC. indicated as: VE, VB and VC, respectively. Two junctions voltages VEB  and VBC  are formed by its three terminals VE VB VC, respectively. For the former junction VEB, forward-biased (VEB > 0) is always needed in order to switch on the device. But for the later junction VBC, both forward-biased (VBC > 0) and reverse-biased (VBC < 0) are possible. The two biasing conditions will result in two complete di_erent operation modes. One is the saturation mode,which is used in digital electronics. The other is the active mode, used in analogue electronics. When VBC is forward-biased(VBC > 0), BJT is used as a switch in digital electronics. When VBC is reverse-biased (VBC < 0), BJT is functioning as an ampli_er in analogue electronics. [11]The established constant values at BJTs three terminals are named as: the bias point or the quiescent point (Q-point) or the DC operating point. The Q-point can be further stabilized against and temperature by replacing the Bias Schemes, such as : voltage divider bias , emitter feedback bias, current source bias...etc. The position of the DC voltage level decides if the waveform of the AC signal that fed in the input port can expand its fully swing( amplification) without being clipped the output port. To put it simply, when a BJT is biased, regardless its operation modes, all its threes terminals are provided with constant values of voltages and currents.[11] From amplifiers prospective, it does not matter what is inside the black box. What does matter is the connection outside the black box.[37] "Biasing" refers to all the external power supply networks or circuits arrangement that connected to its input and output ports to ensure the constant (V, I) levels. Figure 8.2: The _gure on the top left is the input characteristics, which plots IB versus VBE with a constant VCE. Where IB is an exponential function of VBE.The input bias point Qin(VBE, IB) is determined from the intersection between the input load line and the input characteristics. The figure on the top right is the output characteristics, which plots IC versus VCE with IB as the varing parameter. The output bias point Qout(VCE, IC) is determined. The output bias point Qout (VCE, IC) is the intersection between the output load line and the output characteristics. The two schematics below are for DC biasing BJT in CE con_guration. In the measurement of output characteristics, instead of forcing a voltage source VBB to the base, a current source IB is employed. The replacement in the bias current source at the base is to prevent the self-heating effects. 65

Figure 8.3: The graphic analysis of determining the Q-point of the input loop is presented here. Two plots are involved during the analysis process. One is the input characteristics from the the CE con_guration of BJT, which plots the relationship between IB and VBE with a constant VCE. The other is the load line, which is governed from the KVL around the input loop. Both plots intersects at the statics input operating point Qin(VBEQ; IBQ).

Figure 8.4: The graphic analysis of determining the Q-point of the output loop is presented here. Two plots are involved during the analysis process. One is the statics output characteristics from the the CE configuration of BJT, which plots the relationship between IC and VCE with a varying IB. The other is the load line, which is governed from the KVL around the output loop. Both plots intersects at the output operating point Qout(VCEQ; ICQ). Figure 8.5: The chosen biasing level for the class AB power amplifier is near the cutoff regime. Three main steps are involved in solving out the Q point at the output Qout(ICQ, VCEQ). Figure 8.6: The simpli_ed biasing schematic for BJT in CE con_guration is shown above. The values of VBB and VCC are directly provided and manipulated by the DC power supplies. The values of the terminal voltages VE VB VC can be calculated via the voltage drop over the biasing resistances RERB RC. However, due to the internal barrier potentials over pn junctions, the expected values of the junctions voltages VCE VEB VBC might be very different from the actual measured ones. For this purpose, the experimental setup for the measuring BJTs I􀀀V characteristics is required.

Figure 8.7: The conceptional schematic is introduced in the construction of the load line equation at both input and output loops. Where the equivalent piecewise linear model is in replacement of the original BJT symbol.VCC and VBB work as the DC voltage sources to produce its three voltage nodes VB VC VE with constant values.The load line equations of BJT are governed by KVL at the input and the output loops, respectively. Performing graphic analysis with load line is a useful mean which prevents the possible iterative method. Figure 8.8: The operation point Q at the output terminal can be determined by three main steps: (I)the DC input characteristics:(VEB versus IB) (II.)beta (III.)the DC output characteristics:(VCE versus IC). Where VBEQ = ..IBQ = …. ICQ = .. VCEQ = ... DC characterization is prior to AC characterization. This section highlights the importance of an accurate pre-determined DCcompact model.[38] For compact model developers, extraction of the DC parameters is performed before the AC ones. For devices measurement, DC measurement has to be carried out before AC measurement. For modern IC designers, DC analysis needs to be carried out before AC analysis.[39, 4.6.4] For SPICE-like simulators, DC simulation also needs to be swept first and then follows by AC simulation.[40]

From the device-level prospectives, a set of equations which describe the terminal characteristics of DUT are written in a compact model. The equations are solved by SPICE-like simulators. The procedure of establishing equations, describing device's electrical characteristics, in a compact model and have them solved by SPICE-like simulators is termed as: Device Characterization. The fully Characterizations are treated by two independent steps: (1)DC Characterization or DC compact modelling (2)AC Characterization or AC compact modelling. Characterizing a nonlinear electronics component always begins with the characterization of its DC behaviors and follows by the AC one.

From the circuit-level prospectives, Circuit analysis refers to solving a circuit with KVL and KCL. To be more speci_c, it means solving out nodes voltages and branches currents of each element in a circuit. As the source of stimulus can be systematically separated into DC sources and AC sources, the unknown/solutions of the circuit are also separated into DC part and AC part. Analyzing a circuit is treated in two independent means:

(A)DC analysis(B)AC analysis The separation between DC analysis and AC analysis greatly simplified a complex circuit. DC analysis is being carried out before AC analysis. DC analysis determines the Q-point, including each node voltage and branch current. AC analysis gives the frequency response, including bandwidth and gain. Before performing AC Analysis, the DC operating point needed to be calculated from DC analysis _rst. This is to construct a linear small-signal model for the nonlinear component. So, the small signal (AC) response is highly dependent upon the presetting (DC) bias condition, DC simulation in analog SPICE-like simulator, aims for computing the equilibrium points, which are the calculated DC node voltages plus DC branch currents in a circuit. They are the DC solutions of the DC equivalent equation/circuit. A circuit will only reach its equilibrium if its stimulus is off and the independent sources are remain constantly employed. There is an important reason why a given electronics circuit always need to be reduced into a DC equivalent circuit (large-signal model) and followed by an AC equivalent one(small-signal model). It has to do with the present of an active component in the circuit. The active component is a nonlinear element.So, it will have to be linearized. The employment of active elements, like transistors, make the circuit a nonlinear algebra system. Normally, the nonlinear equation can only be solved by means of iterative methods, such as Newton-Raphson algorithm [40]. This algorithm transforms the solutions of the nonlinear equation into a sequence of linear equation. Likely, in linear electronic circuits, the superposition principle skillful separates all the electrical characteristics, voltages and currents, into the DC part and the AC part. The AC signals are superimposed on the DC signals.The two independent quantities, AC quantities and DC quantities, can be determined by means of two independent means in circuit analyses. Firstly, DC analysis is carried out in order to determine DC bias points, which are the DC quantities VE VB VC IE IB IC.The DC analysis are performed when the original circuit is simpli_ed into the equivalent DC circuit. Where all the passive elements are remained in the circuit, but all the reactive elements such as: capacitors and inductors are removed. Secondly, the AC analysis performed on the equivalent AC circuit, which is the so called: the small-signal equivalent circuit. The equivalent AC circuit is executed by removing all the DC sources and replacing transistors with the small-signal models.