BJT Amplifiers: Common Emitters and DC Analysis

If we asked most people about the purpose of the basilar membrane, we might receive answers ranging from something that protects a boat hull from leaking to something about strange lights in the night sky. In all seriousness though, the basilar membrane --in partnership with the cochlea and tiny hair cells--allows all of us--and all our fellow vertebrates--to hear or perceive sound.

With one end stiff and narrow and other end wider and flexible, the basilar membrane becomes stimulated by sine waves. Each wave travels from the stiff, narrow end to the wider, flexible end, increases in amplitude, and then decreases in amplitude. As the vibrations vary in frequency, high frequencies produce peaks near the narrow end and low frequencies peak toward the wide end.

We Have Our Own Amplifiers

While the basilar membrane performs as a frequency analyzer and frequency-tuned delay line, the cochlear mechanically amplifies the movement of the membrane. Amplification occurs as the cochlear enlarges the signal by transferring energy to the signal from an external source.

Amplification is a fundamental part of electronic circuit design. Referring back to the basilar membrane and cochlear, we see a non-linear amplifier because the amplitude of the movement is not proportional when compared to the level of sound pressure. The non-linear amplification produced by our auditory systems gives us the sensitivity that we need when listening to low- and high frequencies.

Linear amplifiers produce an amplified output signal that has the exact shape as the input signal. Small signal amplifiers--such as bipolar junction transistors (BJT) work as linear amplifiers.

What is a Bipolar Junction Transistor, and What Does It Do?

Bipolar Junction Transistors--join three layers of p-type and n-type together to construct either pnp or npn transistors. Taking this an additional step further, an npn transistor has two pn junctions placed back-to-back. One n region (n+) of the transistor receives a heavier doping of charge carriers than the other n region and serves as the emitter for the transistor. The middle, narrow section of p-type material (p) l forms the base of the transistor while the other less doped n region (n) forms the collector of the transistor.

The construction of a BJT takes us back to pn diodes in that the base-emitter junction of an npn transistor operates as a forward-biased diode. Electrons flow from the heavily-doped n+ material to the p-type material and holes move from the p-type material to the n+ region. Once the electrons reach the narrow base region, reverse-biasing of the base-collector junction allows the collector to gather electrons from the emitter. Then, a larger amount of current flows from the collector to the emitter than from an external circuit into the base.

Injecting a small amount of current into the base causes a larger amount of current to flow into the collector. As a result, a small base current controls the much larger collector current. We refer to the bipolar junction transistors as small signal amplifiers because the devices require a small bias voltage to establish the Q-point--or operating point. Without the bias voltage, the transistor cannot increase the amplitude of an ac signal.

Utilizing transistors in your design means finicking with voltage and current requirements.

The Q-point represents a steady-state DC voltage or current--with no signal applied--at a designated transistor terminal. Variations in current and voltage occur around the Q-point in response to a small ac input signal voltage. With all this, the transistor operates as a current-controlled current source.

We Have Something in Common 

We can use three different configurations to achieve amplification with a bipolar junction transistor. While the common-emitter configuration uses the emitter as the common terminal to an ac signal, the common-collector--or emitter follower--amplifiers have the input applied to the base through a coupling capacitor and the output at the emitter. Common-base amplifiers use the base as the common terminal for an ac signal and capacitively couple the input signal to the emitter. The common-base output capacitively couples from the collector to a load resistor.

Common-emitter amplifiers offer high voltage gain and high current gain. In all amplifiers, voltage gain (AV) equals the output voltage divided by the input voltage or:

AV = Vout / Vin

For common-emitter amplifiers, the ac voltage gain equals the ac output voltage at the collector divided by the ac input voltage at the base.

 We measure the current gain (A_i) as the current at the collector (I_C) divided by the total signal current (IS) or:

         Ai = IC / IS

The total signal current is the current produced by the source. In turn, the base current and part of the bias current as it flows through a bias circuit contribute to the total signal current.

Current Gain or Current Loss

Even though common-collector amplifiers only produce a voltage gain of approximately 1, the common-collector configuration gives the benefits of a high input resistance, low output resistance, and a high current gain. The combination of high input resistance and low output resistance allows a common-collector amplifier to function as a buffer that keeps loading effects low if the circuit drives a low-resistance load.

For common-collector amplifiers, the current gain (A_i) equals the sum of the emitter and load currents (I_e) divided by the input current (I_in) or:

Ai = Ie / I in

Common-base amplifiers produce a high voltage gain and a maximum current gain of one. Because common-base amplifiers have a low input resistance, circuit designs will use common-base configurations for communication systems that require source impedance matching.

DC Analysis of BJT Amplifier Circuits

Using the common-emitter amplifier circuit shown in the figure as an example, the use of equivalent circuits assists with analyzing circuits. DC analysis of a common-emitter amplifier circuit begins with determining the dc bias values and then removing coupling and bypass capacitors, the load resistor, and the signal source to produce a dc equivalent circuit by applying Thevenin’s theorem and Kirchoff’s voltage law.

AC analysis of a common-emitter amplifier circuit begins by recognizing the capacitive reactance (XC) remains very low at the signal frequency. By considering XC as equal to zero, reducing the circuit to an ac equivalent circuit requires replacing the three capacitors in the circuit with effective shorts. Then, the analysis continues by replacing the dc source with ground. From the perspective of ac analysis, a dc voltage source has an internal resistance of zero ohms.

Since no ac voltage can develop across the dc source, it serves as an ac ground. Electrically, the ac ground and actual ground exist at the same point. All this reduces the equivalent circuit to three resistors and the transistor. Connecting an ac voltage source to the input of the circuit. Because the AC source voltage has an internal resistance of zero ohms, the source voltage appears at the base of the transistor.

Finding the ac signal voltage at the transistor base requires combining the source resistance (RS), the bias resistance, and the ac input resistance at the base to produce the total input resistance (Rin(tot) ) seen by the ac source connected to the input. Using the voltage divider formula, the signal voltage at the base of the transistor (Vb) equals:

         Vb = (Rin(tot) / RS + Rin(tot) ) VS

With the suite of design and analysis tools from Cadence, you’ll be sure to have everything you need to calculate, simulate, model, layout, and finalize designs using BJT amplifiers. PSpice simulation has an active model library of 34,000 and growing, as well as containing the DC analysis capabilities to accurately and quickly simulate any of your circuit necessities. 

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