2.2. Fundamentals of Signal Amplification: The Linear Circuit

The most fundamental property of a useful electronic voltage amplification device is that it possess a transconductance that leads to the possibility of voltage gain. Transconductance is defined as the ratio of the signal (ac, incremental) current out, i_out ≡ δi_OUT, and the applied input signal voltage, v_in ≡ δv_IN. That is, transconductance g_m is

Equation 2.3

For the BJT, i_OUT ≡ i_C and v_IN ≡ v_BE, while for the NMOS, i_OUT ≡ i_D and v_IN ≡ v_GS. Thus, (2.1) and (2.2) can be used for the BJT and MOSFET, respectively, to obtain an expression for g_m. The results are

Equation 2.4

and

Equation 2.5

I_C and I_D are the dc (bias) currents of the transistors, so for comparison they can be made equal. At room temperature, the thermal voltage is V_T = 26 m. For the MOSFET, V_GS is the gate – source bias voltage and V_tn is the transistor threshold voltage. The difference, as in the denominator of the transconductance expression, could typically be about V_GS – V_tn = 500 mV.

The expression (2.3) suggests the linear model given in Fig. 2.2. Included in the model is an input resistance, r_in, which accounts for the fact that there can be an incremental current flowing into the input terminal for an increment of input voltage. The model applies in general to amplifying devices, including the vacuum tube (VT), BJT, JFET, and MOSFET. There exists a wide range of magnitude of transconductance and input resistance between the devices. The input resistance, though, affects only the loading of the input signal source; otherwise, the relation of (2.3) applies in all cases, and the transconductance is the key to the gain for a given device type. The input resistance is essentially infinite for the vacuum tube and the MOSFET (common source) but can be as low as a few ohms in some configurations for the BJT (e.g., common base).

It is interesting to compare the transconductance of the BJT and MOSFET along with the vacuum tube. We will make a comparison at I_D = I_C = 10 mA (suitable for a vacuum tube) even though transistors would not usually be operated at such high currents, especially in an integrated circuit. Consulting a source of information for a triode 6SN7 (perhaps one of the most common tubes of all time), one deduces from a graphical analysis the plate characteristics that, for example, g_m(VT) = 3 mA/V. From (2.4) and (2.5), we obtain g_m(BJT) = 385 mA/V and g_m(MOSFET) = 40 mA/V with V_GS – V_tn = 500 mV. The BJT is decidedly superior in this respect, and this is one of the factors contributing to the sustained life of the transistor in industry. That is, the BJT amplifier stage can potentially have a much higher voltage gain. The vacuum tube is clearly inferior to both transistors and points to the reason for the need for so many amplification stages in some VT amplifiers.

The output voltage of amplifiers based on any of the devices will depend on the value of the load resistance, R_L, which is added to the circuit of Fig. 2.2 in Fig. 2.3. Note that, in general, R_L is not necessarily an actual resistor but could be an effective resistance, as dictated by the amplifier circuitry that is connected to the output of a given stage, combined with a bias resistor. The output voltage induced across R_L will be

Equation 2.6

The minus sign is a result of the current flowing up through R_L. The signal voltage gain is the incremental output voltage divided by the incremental input voltage such that the gain can readily be obtained from (2.6) as

Equation 2.7

Thus, the gain is directly related to the parameter g_m for a given transistor. In general, a_v can be positive or negative, depending on the terminal configuration. For example, the common base (BJT) and common gate (MOSFET) are positive (noninverting) gain amplifiers.