In another thread, a two stage BJT amplifier was analyzed. I'd like to carry it a bit further and add a single feedback resistor.
I want to show how just the addition of a single feedback resistor, RFB, between the two emitters substantially increases the difficulty of analysis.
The original circuit (first image) can be analyzed for voltage gain a piece at a time, but the addition of the feedback resistor (second image) pretty much requires the analysis to deal with the entire circuit at once. This means setting up a system of equations including all the variables.
In 1952, Jacob Shekel published a paper in the Proceedings of the IRE showing a systematic way of doing this with matrix arithmetic. His method allows calculation of the various gains and impedances from a single admittance matrix.
The schematic shows values for the intrinsic emitter resistances (re1 and re2) that are slightly different from what an exact analysis would give, but I chose to stick with the values that were in the original thread.
Using small signal nodal analysis, there are 5 nodes, numbered in red. I've labeled node 3 at both the collector of Q1 and the base of Q2 as a reminder that they are really the same node. Even though values are shown for the capacitors, assume that they are AC short circuits; zero ohms, in other words.
The transistors are assumed to have infinite intrinsic collector resistance (ro), and zero reverse voltage transfer ratio.
This circuit is a step above the elementary problems often seen in this forum, and I hope the more advanced members will find it interesting.
Let RFB have a value of 2344.06792623 ohms. Calculate the input impedance at node 1 for both circuits. Assume the source Vs (which is an ideal voltage source with zero ohms output impedance) applies a signal to node 1, and calculate the voltage gain from that input to the other 4 nodes.
As a hint, I'll tell you that the overall voltage gain for the circuit without the feedback resistor is 447.21755, and with RFB connected, the voltage gain to node 3 is 109.567.
Try out your analysis skills, using your favorite analysis method, and later I'll show how to do it using Shekel's method. If anyone wants a copy of his paper, post a disguised valid email address, and I'll send you a copy.
I want to show how just the addition of a single feedback resistor, RFB, between the two emitters substantially increases the difficulty of analysis.
The original circuit (first image) can be analyzed for voltage gain a piece at a time, but the addition of the feedback resistor (second image) pretty much requires the analysis to deal with the entire circuit at once. This means setting up a system of equations including all the variables.
In 1952, Jacob Shekel published a paper in the Proceedings of the IRE showing a systematic way of doing this with matrix arithmetic. His method allows calculation of the various gains and impedances from a single admittance matrix.
The schematic shows values for the intrinsic emitter resistances (re1 and re2) that are slightly different from what an exact analysis would give, but I chose to stick with the values that were in the original thread.
Using small signal nodal analysis, there are 5 nodes, numbered in red. I've labeled node 3 at both the collector of Q1 and the base of Q2 as a reminder that they are really the same node. Even though values are shown for the capacitors, assume that they are AC short circuits; zero ohms, in other words.
The transistors are assumed to have infinite intrinsic collector resistance (ro), and zero reverse voltage transfer ratio.
This circuit is a step above the elementary problems often seen in this forum, and I hope the more advanced members will find it interesting.
Let RFB have a value of 2344.06792623 ohms. Calculate the input impedance at node 1 for both circuits. Assume the source Vs (which is an ideal voltage source with zero ohms output impedance) applies a signal to node 1, and calculate the voltage gain from that input to the other 4 nodes.
As a hint, I'll tell you that the overall voltage gain for the circuit without the feedback resistor is 447.21755, and with RFB connected, the voltage gain to node 3 is 109.567.
Try out your analysis skills, using your favorite analysis method, and later I'll show how to do it using Shekel's method. If anyone wants a copy of his paper, post a disguised valid email address, and I'll send you a copy.
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