>> the emitter impedance of a silicon BJT is about 30/I, where I is current in milliAmps
> IIRC emmiter R is 25/I
Scan from an old book on Shockley's Law/Relation.
The answer is KT/q exactly, but various sources give the answer as 25, 26, 27, or 30 milliVolts. Who's right? Where is the sloppy number in such a simple formula?
k is Boltzmann's Constant: http://encyclopedia.thefreedictionary.com/Boltzmann%20constant
"k = 1.380 6503(24) × 10^-23 JK^-1"
q is the charge on the electron: http://encyclopedia.thefreedictionary.com/Elementary%20charge
"The electron has a negative electric charge of 1.602 176 462(63) × 10^-19 Coulomb"
Boltzman's number can be derived in theory, but not in practice. The experimentally observed value is certain to 5 decimal places: 1.38065. The charge on the electron is known to 7 places: 1.6021764.
The Temperature is usually not known to better than 2-place accuracy. And in fact, in semiconductor work at "room temperature", we almost always assume "300 degrees K", which comes to 27 degrees C or 80 degrees F. Warmer than many rooms, but most transistors end up a few degrees warm.
I will assume that the powers-of-ten are right, and the answer is about 20-30mV (NOT say KV or MV or uV).
1.38065*300/1.6021764 = 258.52022, so "the answer" is 25.852mV IF the junction is 300.00 deg K exactly.
It is possible to "know" Shockley's Relation to 5 decimal places for the fundamental constants, but usually only 2 places for the temperature. And in wide-temp-range designs (car-audio, military, etc) the Temperature varies so much that you only have "1-place accuracy".
A "hot" transistor may run 50 degrees C, or 323K, or 1.0766 higher. kT/q is then 27.834mV. Lower when cold, like that Pretenders' gig on New Years in Scotland.
So kT/q and Shockley's Law may be 25 to 29mV, depending how cold/hot we run.
And the transconductance at 1mA is about 1mA/26mV= 38,462 microMhos, 0.03846 Mhos (or Siemens). The old unit "Mho" reminds us that transconductance is just an upside down resistance, with value at 1mA of 25 to 29 ohms depending how cool/hot we are.
That's just what the charges inside the junction do. From outside the transistor, we see ohmic losses in the body of the die between the junction and the contact; also the bond-wire. If you run above about 1% of the transistor's rated current (1mA on a "100mA" transistor), these start to bend Shockley's Law up to 30mV, 40mV, or more.
In amplifier design, we probably do not want to let the gain vary with absolute temperature. True, it only varies about 1dB over the range of temperatures we usually find musicians working in (those Scots are crazy), but usually we stuff some resistors in or around the transistor and let them dominate the gain. We only need a ballpark estimate of Shockley's Relation so we can be sure the resistors really DO dominate the gain.
Since I don't know the temperature EXACTLY, and don't know the ohmic losses, and "3" is a lot easier to find on a slide-rule than "26", I always figure "30mV" unless I know the transistor is working close to (over 1%) its maximum rating. It is "conservative": I may get a little more gain than I figure. And hey: my "30mV" is no worse than the convenient assumption that Temperature is "300K". 297K might be the "exact" temp on a certain day and place and function, but "300K" is so much more convenient.
> IIRC emmiter R is 25/I
Scan from an old book on Shockley's Law/Relation.
The answer is KT/q exactly, but various sources give the answer as 25, 26, 27, or 30 milliVolts. Who's right? Where is the sloppy number in such a simple formula?
k is Boltzmann's Constant: http://encyclopedia.thefreedictionary.com/Boltzmann%20constant
"k = 1.380 6503(24) × 10^-23 JK^-1"
q is the charge on the electron: http://encyclopedia.thefreedictionary.com/Elementary%20charge
"The electron has a negative electric charge of 1.602 176 462(63) × 10^-19 Coulomb"
Boltzman's number can be derived in theory, but not in practice. The experimentally observed value is certain to 5 decimal places: 1.38065. The charge on the electron is known to 7 places: 1.6021764.
The Temperature is usually not known to better than 2-place accuracy. And in fact, in semiconductor work at "room temperature", we almost always assume "300 degrees K", which comes to 27 degrees C or 80 degrees F. Warmer than many rooms, but most transistors end up a few degrees warm.
I will assume that the powers-of-ten are right, and the answer is about 20-30mV (NOT say KV or MV or uV).
1.38065*300/1.6021764 = 258.52022, so "the answer" is 25.852mV IF the junction is 300.00 deg K exactly.
It is possible to "know" Shockley's Relation to 5 decimal places for the fundamental constants, but usually only 2 places for the temperature. And in wide-temp-range designs (car-audio, military, etc) the Temperature varies so much that you only have "1-place accuracy".
A "hot" transistor may run 50 degrees C, or 323K, or 1.0766 higher. kT/q is then 27.834mV. Lower when cold, like that Pretenders' gig on New Years in Scotland.
So kT/q and Shockley's Law may be 25 to 29mV, depending how cold/hot we run.
And the transconductance at 1mA is about 1mA/26mV= 38,462 microMhos, 0.03846 Mhos (or Siemens). The old unit "Mho" reminds us that transconductance is just an upside down resistance, with value at 1mA of 25 to 29 ohms depending how cool/hot we are.
That's just what the charges inside the junction do. From outside the transistor, we see ohmic losses in the body of the die between the junction and the contact; also the bond-wire. If you run above about 1% of the transistor's rated current (1mA on a "100mA" transistor), these start to bend Shockley's Law up to 30mV, 40mV, or more.
In amplifier design, we probably do not want to let the gain vary with absolute temperature. True, it only varies about 1dB over the range of temperatures we usually find musicians working in (those Scots are crazy), but usually we stuff some resistors in or around the transistor and let them dominate the gain. We only need a ballpark estimate of Shockley's Relation so we can be sure the resistors really DO dominate the gain.
Since I don't know the temperature EXACTLY, and don't know the ohmic losses, and "3" is a lot easier to find on a slide-rule than "26", I always figure "30mV" unless I know the transistor is working close to (over 1%) its maximum rating. It is "conservative": I may get a little more gain than I figure. And hey: my "30mV" is no worse than the convenient assumption that Temperature is "300K". 297K might be the "exact" temp on a certain day and place and function, but "300K" is so much more convenient.