**Transistor Models and Parameters:**

**T-Equivalent Circuit –** Because a transistor consists of two pn-junctions with a common centre block, it should be possible to use two pn-junction ac equivalent circuits as the Transistor Models and Parameters. Figure 6-9 shows the ac equivalent circuit for a transistor connected in common-base configuration. Resistor r_{e} represents the BE junction resistance, r_{c} represents the CB junction resistance, and r_{b} represents the resistance of the base region which is common to both junctions. Junction capacitances C_{BE} and C_{BC} are also included.

If the Transistor Models and Parameters equivalent circuit is simply left as a combination of resistances and capacitances, it could not account for the fact that most of the emitter current flows out of the collector terminal as collector current. To represent this, a current generator is included in parallel with r_{c} and C_{BC}. The current generator is given the value αI_{e}, where, α = I_{c}/I_{e}.

The complete circuit is known as the T-equivalent circuit, or the r-parameter equivalent circuit. The equivalent circuit can be rearranged in common-emitter or common-collector configuration.

The currents in Fig. 6-9 are designated I_{b}, I_{c}, and I_{e} (instead of I_{B},I_{C}, and I_{E}) to indicate that they are ac quantities rather than dc. The circuit parameters r_{c}, r_{b}, r_{e}, and α, are also ac quantities.

**r-Parameters:**

Referring to Fig. 6-9, r_{e} represents the ac resistance of the forward-biased BE junction, so it has a low resistance value, (typically 25 Ω). The resistance of the reverse-biased CB junction (r_{c}) is high, (typically 100 kΩ to 1 MΩ). The base region resistance (r_{b}) depends upon the doping density of the base material. Usually, r_{b} ranges from 100 Ω to 300 Ω.

C_{BE} is the capacitance of a forward-biased pn-junction, and C_{BC} is that of a reverse-biased junction. At medium and low frequencies the junction capacitances may be neglected. Instead of the current generator (αI_{e}) in parallel with r_{c}, a voltage generator (αI_{e}r_{c}) may be used in series with r_{c}. Two transistor r-parameter models are shown in Fig. 6-10.

**Determination of r**_{e}:

_{e}:

Because r_{e} is the ac resistance of the BJT forward-biased base-emitter junction, it can be determined from a plot of I_{E} versus V_{BE}. As illustrated in Fig. 6-11,

This is similar to the determination of the dynamic resistance (r_{d}) for a forward-biased diode. Also like the case of a diode, the ac resistance for the transistor BE junction can be calculated in terms of the current crossing the junction.

As in the case of r′_{d} for a diode, r’_{e} does not include the resistance of the device semiconductor material. Consequently, r’_{e} is slightly smaller than the actual measured value of r_{e} for a given transistor.

Equation 6-2 applies only to transistors at a temperature of 25°C. For determination of r’_{e} at higher or lower temperatures, the equation must be modified.

**h-Parameters:**

It has been shown that Transistor Models and Parameters circuits can be represented by an r-parameter or T-equivalent circuit. In circuits involving more than a single transistor, analysis by r-parameters can be virtually impossible. The hybrid parameters, or h-parameters are much more convenient for circuit analysis. These are used only for ac circuit analysis, although dc current gain factors are also expressed as It-parameters. Transistor h-parameter models simplify transistor circuit analysis by separating the input and output stages of a circuit to be analyzed.

In Fig. 6-12 a common-emitter h-parameter equivalent circuit is compared with a common-emitter r-parameter circuit. In each case an external collector resistor (R_{C}) is included, as well as a signal source voltage (v_{s}) and source resistance (r_{s}). Note that the output current generator in the r-parameter circuit has a value of αI_{e}, which equals βI_{b}.

The input to the h-parameter circuit is represented as an input resistance (h_{ie}) in series with a voltage source (h_{re}υ_{ce}). Looking at the r-parameter circuit, it is seen that a change in output current I_{c} causes a voltage variation across r_{e}. This means that a voltage is fed back from the output to the input. In the h-parameter circuit this feedback voltage is represented as the portion h_{re} of the output voltage υ_{ce}. The parameter h_{re} is appropriately termed the **reverse voltage transfer ratio**.

The output of the h-parameter circuit is represented as an output resistance (1/h_{oe}) in parallel With a current generator (h_{fe}I_{b}), where I_{b} is the (input) base current. So, h_{fe}I_{b} is produced by the input current I_{b}, and it divides between the device output resistance 1/h_{oe} and the collector resistor R_{C}. I_{c} is the current passed to R_{C}. This compares with the r-parameter equivalent circuit, where some of the generator current (βI_{b}) flows through r_{c}. The current generator parameter (h_{fe}) is termed the **forward transfer current ratio**. The output conductance is h_{oe}, so that 1/h_{oe} is a resistance.

**r**_{π} Equivalent Circuit:

_{π}Equivalent Circuit:

An approximate h-parameter model for a transistor CE circuit is shown in Fig. 6-13(a). In this case, the feedback generator (h_{re}υ_{ce} in Fig. 6-12(b)) is omitted. The effect of h_{re}υ_{ce} is normally so small that it can be neglected for most practical purposes.

The approximate h-parameter circuit is reproduced in Fig. 6-13(b) with the components labelled as r-parameters; r_{π} = h_{ie}, βI_{b} = h_{fe}I_{b}, and r_{c} =1/h_{oe}. This circuit, known as a hybrid-π model, is sometimes used instead of the h-parameter circuit.

**Definition of h-Parameters:**

The e in the subscript of h_{ie} identifies the parameter as a common-emitter quantity, and the i signifies that it is an input resistance. Common-base and common-collector input resistances are designated h_{ib} and h_{ic}, respectively.

As an ac input resistance, h_{ie} can be defined as the ac input voltage divided by the ac input current.

This is usually stated as,

This means that the collector-emitter voltage (V_{CE}) must remain constant when h_{ie} is measured.

The input resistance can also be defined in terms of changes in dc levels;

Equation 6-5 can be used for determining h_{ie} from the transistor common-emitter input characteristics. As illustrated in Fig. 6-14, ΔV_{BE} and ΔI_{B} are measured at one point on the characteristics, and h_{ie} is calculated.

The reverse transfer ratio h_{re} can also be defined in terms of ac quantities, or as the ratio of dc current changes. In both cases, the input current (I_{B}) must be held constant.

The forward current transfer ratio h_{fe} can similarly be defined in terms of ac quantities, or as the ratio of dc current changes. In both cases, the output voltage (V_{CE}) must be held constant.

Equation 6-8 can be used to determine h_{fe} from the CE current gain characteristics. Figure 6-15 shows the measurement of ΔI_{C} and ΔI_{B} at one point on the characteristics for the h_{fe} calculation.

The output conductance, h_{fe}, is the ratio of ac collector current to ac collector-emitter voltage, and its value can be determined from the common emitter output characteristics (see Fig. 6-16).

**Common-Base and Common-Collector h-Parameter:**

The common-base and common-collector h-parameters are defined similarly to common-emitter h-parameters. They may also be derived from the CB and CC characteristics. Common-base parameters are identified as h_{ib}, h_{fb}, etc., and common-collector parameters are designated h_{ic}, h_{fc}, and so on.

**Parameters Relationships:**

Device manufacturers do not list the values of all parameters on transistor data sheets. Usually, only the CE h-parameters are stated. However, CB and CC h-parameters can be determined from the CE h-parameters. r-parameters can also be calculated from the CE h-parameters. Table 6-1 shows the parameter relationships.