- #1
LickMyEyeball
- 23
- 1
Hello,
I am reading The Art of Electronics, and I have two specific questions regarding examples it has introduced. I am dealing with bipolar transistors the current chapter. I think my questions mostly stem from not understanding concepts.
The text has introduced the technique of 'bootstrapping'. The circuit is the first image attached to this post. While I understand that bootstrapping is meant to increase the input impedence seen by the signal source, I do not understand how it works.
In particular, R3 is very strange to me, because both its ends are connected to the same node. Whether I approach this circuit from a DC mindset (Capacitors acting as open circuits, or having an effectively infinite impedence), or an AC mindset, the inclusion of R3 seems irrelevant to the circuit. I see R3 as irrelevant because it separates no nodes from one another in the circuit, and neither does R3 connect anything which wasn't already directly connected.
The text tries to illustrate the operation of the circuit by showing that the current through R3 is zero. This much seemed obvious to me. Why the input impedence would be approximately infinite (the text implies this is the case because of R3's current being zero)? If a time-varying signal is applied, again, why would R3 be relevant when it has been shorted like in the image?My second question deals with a common-emmitter amplifier. I understand how this circuit works. Additionally, I can monkey my way through the process of selecting the values for resistors and caps and understand the rationale behind it... except for one thing. When alternative paths are included at the emmitter (one path with a cap for the signal, the other lone resistor being for the DC bias 'signal'), I do not understand why the capacitor's value is determined the way it is. Referring to the image included, I would like to tell you all that there is very often a pair of resistors R1 and R2 which form a voltage divider. The base connects between the two resistors.
The capacitor is calculated to place the 3db point at a given frequency on a Bode (gain vs. frequency) plot, but the question is what is the R value we include when calculating 1/(2*pi*f*R)? To me, this would the impedence from the capacitors perspective, looking into the circuit.
To me, this would be ((R3//Re)+re)//(R1//R2)/beta. In words, I think I would reflect the resistors in the voltage divider (R1//R2) across the transistor (remembering to divide by beta), add the internal 'resistance' re because it is in series (here re is the reciprocal of the transconductance, I think), then because Re is grounded put it in parallel too, then FINALLY, add R3 because it is in series to the capacitor.
The text determines that the correct value of R should be R3 + re. Nothing else.
Even if the voltage divider network is omitted due to becoming smaller when it is brought across the transistor (Rdivider/Beta)... should Re still not be included in the calculation by putting it in parallel?
Please keep in mind that I am an absolute beginner and examples like this make me think I do not know how to Thevenin properly yet, which is exactly what I do when determining Zin or Zout (are low/high pass filters special and subtlely different? Why is a simple Thevenin not sufficient if they really are different?)
Thank you for reading my novel, I have done my best to explain my interpretations and questions clearly.http://imgur.com/yrMpFTq
http://imgur.com/aGgevaF
If my images have not been included properly, the links are as follows:
bootstrapper:
http://imgur.com/yrMpFTq
amplifier:
http://imgur.com/aGgevaF
I am reading The Art of Electronics, and I have two specific questions regarding examples it has introduced. I am dealing with bipolar transistors the current chapter. I think my questions mostly stem from not understanding concepts.
The text has introduced the technique of 'bootstrapping'. The circuit is the first image attached to this post. While I understand that bootstrapping is meant to increase the input impedence seen by the signal source, I do not understand how it works.
In particular, R3 is very strange to me, because both its ends are connected to the same node. Whether I approach this circuit from a DC mindset (Capacitors acting as open circuits, or having an effectively infinite impedence), or an AC mindset, the inclusion of R3 seems irrelevant to the circuit. I see R3 as irrelevant because it separates no nodes from one another in the circuit, and neither does R3 connect anything which wasn't already directly connected.
The text tries to illustrate the operation of the circuit by showing that the current through R3 is zero. This much seemed obvious to me. Why the input impedence would be approximately infinite (the text implies this is the case because of R3's current being zero)? If a time-varying signal is applied, again, why would R3 be relevant when it has been shorted like in the image?My second question deals with a common-emmitter amplifier. I understand how this circuit works. Additionally, I can monkey my way through the process of selecting the values for resistors and caps and understand the rationale behind it... except for one thing. When alternative paths are included at the emmitter (one path with a cap for the signal, the other lone resistor being for the DC bias 'signal'), I do not understand why the capacitor's value is determined the way it is. Referring to the image included, I would like to tell you all that there is very often a pair of resistors R1 and R2 which form a voltage divider. The base connects between the two resistors.
The capacitor is calculated to place the 3db point at a given frequency on a Bode (gain vs. frequency) plot, but the question is what is the R value we include when calculating 1/(2*pi*f*R)? To me, this would the impedence from the capacitors perspective, looking into the circuit.
To me, this would be ((R3//Re)+re)//(R1//R2)/beta. In words, I think I would reflect the resistors in the voltage divider (R1//R2) across the transistor (remembering to divide by beta), add the internal 'resistance' re because it is in series (here re is the reciprocal of the transconductance, I think), then because Re is grounded put it in parallel too, then FINALLY, add R3 because it is in series to the capacitor.
The text determines that the correct value of R should be R3 + re. Nothing else.
Even if the voltage divider network is omitted due to becoming smaller when it is brought across the transistor (Rdivider/Beta)... should Re still not be included in the calculation by putting it in parallel?
Please keep in mind that I am an absolute beginner and examples like this make me think I do not know how to Thevenin properly yet, which is exactly what I do when determining Zin or Zout (are low/high pass filters special and subtlely different? Why is a simple Thevenin not sufficient if they really are different?)
Thank you for reading my novel, I have done my best to explain my interpretations and questions clearly.http://imgur.com/yrMpFTq
http://imgur.com/aGgevaF
If my images have not been included properly, the links are as follows:
bootstrapper:
http://imgur.com/yrMpFTq
amplifier:
http://imgur.com/aGgevaF