bipolar_transist

# bipolar_transist - AMPLIFIERS A circuit containing only...

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AMPLIFIERS A circuit containing only capacitors, amplifiers (transistors) and resistors may resonate. A circuit containing only capacitors and resistors may not. Why does amplification permit resonance in a circuit with only one kind of storage element? Amplification arises from static behavior, not dynamics and energy storage. Amplification is fundamentally dissipative. P output P supply P output = P supply + P input - P dissipated Amplifiers are basically multiport resistors How does the addition of a (multiport) dissipator enable resonance? Mod. Sim. Dyn. Sys. Amplifiers page 1

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W E WILL SEE THAT • Amplification is fundamentally a non-equilibrium phenomenon. • Resistors far from equilibrium may contain a "hidden" junction structure that includes a gyrator. • This gyrator can cause resonance with only one kind of storage element. Mod. Sim. Dyn. Sys. Amplifiers page 2
NODICITY Electrical amplifiers are nodic. Assuming conductance causality the equations of the three-port resistor may be written as follows. f 1 = Γ 1 (e 1 ,e 2 ,e 3 ) f 2 = Γ 2 (e 1 ,e 2 ,e 3 ) f 3 = Γ 3 (e 1 ,e 2 ,e 3 ) Mod. Sim. Dyn. Sys. Amplifiers page 3

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Nodicity means that the efforts and flows at the ports are constrained so that they satisfy two conditions: (1) Continuity of flow : The sum of flows into the system is zero. This means that the element behaves as a node characterized by a Kirchhoff current law. (Note the implicit assumption of the "power positive in" sign convention) (2) Relativity of effort : Each flow depends only on the difference of applied efforts. The same effort may be added to all inputs without changing the output. Mod. Sim. Dyn. Sys. Amplifiers page 4
The constitutive equations of a nodic three-port resistor may be written as follows. f 1 = Γ 1 [(e 1 – e 3 ),(e 2 – e 3 )] f 2 = Γ 2 [(e 1 – e 3 ),(e 2 – e 3 )] f 3 = –(f 1 + f 2 ) Nodicity implies that the behavior of the element is independent of any absolute reference frame. A nodic three-port (n-port) contains an “embedded” two-port (n-1-port) characterized by two constitutive equations (not three). Mod. Sim. Dyn. Sys. Amplifiers page 5

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A semi-conductor diode has two ports (two wires) but, in common with all electronic devices it is well described as a nodic element and is characterized quite accurately by a single constitutive equation such as i = I s [e (e 1 –e 2 )/V t – 1] where V t : thermal voltage = kT/q = 25.3 mV at 20°C k: Boltzmann's constant T: absolute temperature q: charge on the electron I s : reverse saturation current Note that the element satisfies the conditions for nodicity even though both the thermal voltage and the reverse saturation current depend on absolute temperature. Mod. Sim. Dyn. Sys.
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bipolar_transist - AMPLIFIERS A circuit containing only...

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