Claude,
Vbe exists to lower the barrier voltage caused by the uncovered charges, which in turn are caused by the diffusion of electrons from the n-material and holes from the p-material. An ideal diode cannot exist as a bipolar junction because of this barrier voltage. I already acknowledged that energy is involved from a outside source in creating and maintaining Vbe. But this does not detract from the fact that it is the Vbe voltage that will control Ib and Ic, because Vbe is what lowers the barrier voltage. It also ties in with the equations from Sedra and Smith. And any claim about what occurs first does not determine what is the control
I don't follow your reasoning, and why you insist on postulating about perfect semiconductors. Bipolar transistors will never be perfect due to their barrier voltage. The collector exists to isolate the output from the input. Without the collector, the output voltage would intefere with the input signal. Yes, the base if made thin so as to not capture any more base current that necessary, and any it does catch is wasted.
Sedra and Smith say that Ic is exponentially related to Vbe. The reason Vbe exists is to lower the barrier voltage. That is the basis for regarding it as a VC device with respect to causality.
That relationship is true, but it is not the causing factor.
Ratch
But how does Vbe relate to being "the rudder". Vbe exists because p-n jcns are not ideal. An ideal revtifying jcn would be open in reverse, short in forward direction. If a semiconductor w/ zero bandgap energy existed, charges entering the emitter would transit through the base onward to the collector. The no. of e- collected is controlled by the no. of e- emitted. After Ib/Ie are changed by Sue, Ic increases as a result, but a little later, Vbe increases. But Vbe increasing is not the control mechanisn. In order to supply more electrons for the emitter to emit, work must be done. When Sue cranks it up, it is the increased current/voltage from the mic resposible for Ie/Ib increasing. As a consequence, Vbe increases after the fact, but Ic has already begun to increase w/o Vbe increasing yet.
Vbe exists to lower the barrier voltage caused by the uncovered charges, which in turn are caused by the diffusion of electrons from the n-material and holes from the p-material. An ideal diode cannot exist as a bipolar junction because of this barrier voltage. I already acknowledged that energy is involved from a outside source in creating and maintaining Vbe. But this does not detract from the fact that it is the Vbe voltage that will control Ib and Ic, because Vbe is what lowers the barrier voltage. It also ties in with the equations from Sedra and Smith. And any claim about what occurs first does not determine what is the control
The intermediate variable at the jcn is Ie. Although Ib & Vbe change as well, only Ie contributes to Ic. Ib & Vbe are necessary because perfect semiconductors cannot be produced. The Ie is not controlled by the Vbe. The eqns you keep referencing are functional relations, not causal.
Start w/ the n-p-n as a pair of back to back diodes. The upper diode is the b-c jcn, described by Shockley's diode eqn
Ic = Ics*exp((Vbc/Vt)-1). Since Vbc is negative, a very small Ic exists, leakage of the reverse biased p-n b-c jcn.
The lower p-n jcn, b-e is forward biased. So we have
Ie = Ies*exp(Vbe/Vt)-1), a large current since Vbe is positive.
If the base region was very wide, say 1.0 mm, the above relations are what we get. Ie = Ib, a large value, w/ Ic being a small leakage.
But if the base region is made ultra thin, say 1.0 um, we find that Ic measures almost as large as Ie, w/ Ib being quite small, Ib = Ie-Ic. Instead of 2 mere series diodes, we have transistor action. The b-c jcn is reverse biased, but Ic is almost Ie. The Shockley eqn needs another term. The additional current is Ic = alpha*Ie. So we get
Ic = alpha*Ies*exp((Vbe/Vt)-1) + Ics*exp((Vbc/Vt)-1).
But sonce the 2nd term is much smaller than the 1st, we round off & use Ic = alpha*Ies*exp((Vbe/Vt)-1). Also, alpha is very near to unity, so some texts omit alpha, w/ the resulting eror being 1 to 2%.
I don't follow your reasoning, and why you insist on postulating about perfect semiconductors. Bipolar transistors will never be perfect due to their barrier voltage. The collector exists to isolate the output from the input. Without the collector, the output voltage would intefere with the input signal. Yes, the base if made thin so as to not capture any more base current that necessary, and any it does catch is wasted.
The Vbe eqn, which I've called eqn 2), is derived from Shockley's diode eqn, plus the eqn 3), the transistor action eqn. Ie & Vbe do have a functional relationship per eqn 2). But Vbe is directly related to Ib & Ie, but indirectly related to Ic. Ie has a direct relation w/ Ic per eqn 3).
In order for Ic to change, all that is needed is a change in Ie. In the process, Ib & Vbe change as well, but that is not what changes Ic. Ic starts increasing prior to Vbe increasing, & Vbe continues to increase after Ic has settled
Sedra and Smith say that Ic is exponentially related to Vbe. The reason Vbe exists is to lower the barrier voltage. That is the basis for regarding it as a VC device with respect to causality.
No brainer at all. Transistor action is Ic = alpha*Ie. Any test w/ instruments will affirm. A good software simulator might show this, but the models have to be really accurate. Low end packages won't work.
That relationship is true, but it is not the causing factor.
Ratch
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