Claude Abraham
Member
Drs. Ebers & Moll equivalent bjt circuit 1954 as cccs
This excerpt is from the Dec. 1954 issue of IRE journal, by Drs. Ebers and Moll. I refer you to "fig. 5, equivalent circuit of junction transistor valid in regions I and II, and the small signal equivalent circuit."
In the top figure, the emitter current Ie is depicted as related to "phi_e" (Drs. Ebers-Moll used this for "Vbe") per Shockley's exponential equation. This is expressed in the upper left. In the lower left the 2nd component of emitter current is expressed solely in terms of alpha_n, alpha_i, and Ieo, the emitter current representing the collector leakage current in the upside down bjt, where emitter and collector are swapped.
For Ic, please observe. Collector current Ic is expressed in 2 components, the lower is "Ico" which is collector leakage current due to c-b junction reverse bias, a small value. Most bjt users are familiar with Ico.
The upper expression details Ic as a current source whose control parameter is given as "alpha_n*Ie". Alpha_n is alpha in "normal mode" i.e. the right side up bjt. "Alpha_i" is the inverse alpha value for upside down bjt.
Refer to the lower figure, The 3 bjt regions are modeled as resistances re, rb, and rc. The collector has a CCCS across rc. This current controlled current source is controlled by Ie with alpha_n as a parameter. Let me emphasize that in the infancy of the bjt, the current which controls Ic is not Ib, but rather Ie.
This is a very old paper, and much new info regarding bjt operation exists now. But 1 fact that cannot be refuted is that the number of charge carriers "collected" in a time span by the collector, is dictated by the number of carriers "emitted" by the emitter in that time span.
Of course, Vbe, Ies, Ics, Vbc, Vbe, etc., are involved. I never attempted to deny the role that other factors play. Although the E-M equations express Ie/Ic as a function of Vbe and Vbc, they model the collector current as a current source controlled by Ie. The rc resistance across the current source accounts for Early effect. The Ic value does vary with Vce, so it is a current source with less than infinite shunt resistance. The rc inclusion accounts for Early effect.
I have to concur because Shockley's equation is all important but it describes the I-V relation in any p-n junction, be it LED, rectifier, JFET g-s terminals, etc. But bjt action occurs by emitter carriers emitted, transiting through base, and collected by collector. If base region is super wide, say 1.0 mm, a huge number of holes would transit from base to emitter, even more electrons from emitter towards base. Very few electrons would reach the collector. Ib would about equal Ie, and Ic is small, merely leakage across reverse biased c-b junction.
Shockley's equation says that the b-e junction exhibits an exponential I-V relation, or a logarithmic V-I relation, however you look at it. It certainly is correct. But with alpha near zero or at zero, there is zero transistor action. I believe that Drs. Ebers and Moll studied the device and ascertained that this relation:
Ic = alpha*Ie,
is the key to understanding bjt functioning. The Shockley is very important is it relates I to V. All amp stages possess both voltage and current gain. Alpha and beta give us the upper limit on current gain. The gm factor is derived from Shockley, and gm is the upper limit for stage transconductance. Transconductance times load resistance is overall stage voltage gain.
Shockley diode equation and gm provide useful info on the amp stage voltage gain ability. Beta and alpha convey current gain capability. They are both important since active devices have both greater than unity. The ability to increase both V & I is what makes active devices, such as the bjt, so attractive.
I see no reason to disagree with Drs. Ebers and Moll. BR.
This excerpt is from the Dec. 1954 issue of IRE journal, by Drs. Ebers and Moll. I refer you to "fig. 5, equivalent circuit of junction transistor valid in regions I and II, and the small signal equivalent circuit."
In the top figure, the emitter current Ie is depicted as related to "phi_e" (Drs. Ebers-Moll used this for "Vbe") per Shockley's exponential equation. This is expressed in the upper left. In the lower left the 2nd component of emitter current is expressed solely in terms of alpha_n, alpha_i, and Ieo, the emitter current representing the collector leakage current in the upside down bjt, where emitter and collector are swapped.
For Ic, please observe. Collector current Ic is expressed in 2 components, the lower is "Ico" which is collector leakage current due to c-b junction reverse bias, a small value. Most bjt users are familiar with Ico.
The upper expression details Ic as a current source whose control parameter is given as "alpha_n*Ie". Alpha_n is alpha in "normal mode" i.e. the right side up bjt. "Alpha_i" is the inverse alpha value for upside down bjt.
Refer to the lower figure, The 3 bjt regions are modeled as resistances re, rb, and rc. The collector has a CCCS across rc. This current controlled current source is controlled by Ie with alpha_n as a parameter. Let me emphasize that in the infancy of the bjt, the current which controls Ic is not Ib, but rather Ie.
This is a very old paper, and much new info regarding bjt operation exists now. But 1 fact that cannot be refuted is that the number of charge carriers "collected" in a time span by the collector, is dictated by the number of carriers "emitted" by the emitter in that time span.
Of course, Vbe, Ies, Ics, Vbc, Vbe, etc., are involved. I never attempted to deny the role that other factors play. Although the E-M equations express Ie/Ic as a function of Vbe and Vbc, they model the collector current as a current source controlled by Ie. The rc resistance across the current source accounts for Early effect. The Ic value does vary with Vce, so it is a current source with less than infinite shunt resistance. The rc inclusion accounts for Early effect.
I have to concur because Shockley's equation is all important but it describes the I-V relation in any p-n junction, be it LED, rectifier, JFET g-s terminals, etc. But bjt action occurs by emitter carriers emitted, transiting through base, and collected by collector. If base region is super wide, say 1.0 mm, a huge number of holes would transit from base to emitter, even more electrons from emitter towards base. Very few electrons would reach the collector. Ib would about equal Ie, and Ic is small, merely leakage across reverse biased c-b junction.
Shockley's equation says that the b-e junction exhibits an exponential I-V relation, or a logarithmic V-I relation, however you look at it. It certainly is correct. But with alpha near zero or at zero, there is zero transistor action. I believe that Drs. Ebers and Moll studied the device and ascertained that this relation:
Ic = alpha*Ie,
is the key to understanding bjt functioning. The Shockley is very important is it relates I to V. All amp stages possess both voltage and current gain. Alpha and beta give us the upper limit on current gain. The gm factor is derived from Shockley, and gm is the upper limit for stage transconductance. Transconductance times load resistance is overall stage voltage gain.
Shockley diode equation and gm provide useful info on the amp stage voltage gain ability. Beta and alpha convey current gain capability. They are both important since active devices have both greater than unity. The ability to increase both V & I is what makes active devices, such as the bjt, so attractive.
I see no reason to disagree with Drs. Ebers and Moll. BR.