Hi,
I'm reading the Bob Cordel Designing Audio Power Amplifiers (2011) interesting book and I have a doubt:
on page 37 (see attachment) it is said that the output impedance of the current source in the figure is 290Kohm. I get a different result. It should be Ro=ro(1+gm*Re) which is equal to approximately 1900Kohm, considering VA approximately 100V. Can anyone explain to me?
I'm reading the Bob Cordel Designing Audio Power Amplifiers (2011) interesting book and I have a doubt:
on page 37 (see attachment) it is said that the output impedance of the current source in the figure is 290Kohm. I get a different result. It should be Ro=ro(1+gm*Re) which is equal to approximately 1900Kohm, considering VA approximately 100V. Can anyone explain to me?
Attachments
It looks like you may not have included the hybrid-pi transistor model element "r_pi" in your analysis. In the current source circuit of post #1, the transistor base is at AC ground, so "r_pi" is connected between emitter and ground. Thus r_pi is effectively connected in parallel with the emitter resistor "Re". Your expression for output impedance does not include either "r_pi" or its definition, (Beta/gm).
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Attachments
The discrepancy originates from the Thevenin equivalent resistance of the base divider.
It is easy to understand, either using the hard math method, or just reasoning. 20~30yrs ago, I would have presented a nice sheet filled with lines of equations, but I have become a LOF (lazy old fart), and I prefer softer methods whenever possible.
I am still able to scribble equations when required, but I prefer a less frontal attack, which also has the advantage of being intuitive and readily understandable.
Without the base divider, the potential would remain fixed at 2.7V, whatever.
When the Thevenin equivalent is included, the resistance seen by the base is ~5K.
You can see the Early effect as an increase in β with Vce; if β increases, Ib decreases meaning the burden on the divider decreases, which increases the base voltage; the emitter follows the base voltage, meaning a voltage increase across R1, increasing the emitter and collector currents.
This current increase with collector voltage translates into a parallel resistance at the collector.
To get your calculated Ro value, you need a pure common base stage, ie. make the Thevenin resistance of the divider negligible
thanks, yes with LTspice the same value will come but being an old electronic engineer I would have liked to understand with the equations how we can reach Bob's 290Kohm 🤔
Marcel is definitely not a LOF!
Having both methods expounded is nice, but they aren't exactly two sides of the same coin.
Marcel's calculations are based on the linear, small signal model, whilst my reasoning is based on a non-linear effect, the Early effect
Having both methods expounded is nice, but they aren't exactly two sides of the same coin.
Marcel's calculations are based on the linear, small signal model, whilst my reasoning is based on a non-linear effect, the Early effect
Thanks, butthe reasoning is similar to mine (in which I approximated). The point is that it is not the value indicated by Bob Cordell (around 290K) but rather around 1900K
Is that a reply to me or to Elvee? I suspect that rpi/(rpi + Rdiv + RE) isn't even close to 1.
Assuming beta is about 130, which I based on a graph in the NXP datasheet of the transistor that actually shows hFE rather than hfe, I end up with an impedance that is even lower than LTSpice's impedance:
The calculated impedance is at the bottom of the middle column, the impedance with zero impedance voltage divider is in the right column. I used LibreOffice Calc rather than pencil and paper or a slide rule, which shows that I'm in fact quite lazy.
Tweaking beta to get the value closer to 290 kohm, I get this:
Even when Rdiv = 0, the impedance is less than the simple approximation predicts, because rpi is effectively in parallel with the feedback resistor RE, reducing the efficacy of the local series feedback.
When Rdiv > rpi, only a part of the voltage fluctuations across RE actually drives the controlled source - it's like the transconductance is reduced from gm to gm rpi/(rpi + Rdiv). This again reduces the efficacy of the local series feedback.
The calculated impedance is at the bottom of the middle column, the impedance with zero impedance voltage divider is in the right column. I used LibreOffice Calc rather than pencil and paper or a slide rule, which shows that I'm in fact quite lazy.
Tweaking beta to get the value closer to 290 kohm, I get this:
Even when Rdiv = 0, the impedance is less than the simple approximation predicts, because rpi is effectively in parallel with the feedback resistor RE, reducing the efficacy of the local series feedback.
When Rdiv > rpi, only a part of the voltage fluctuations across RE actually drives the controlled source - it's like the transconductance is reduced from gm to gm rpi/(rpi + Rdiv). This again reduces the efficacy of the local series feedback.
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