Author Topic: Bypassed emitter on Common Emitter Amplifier  (Read 176 times)

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Offline Moriambar

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Bypassed emitter on Common Emitter Amplifier
« on: April 11, 2020, 03:04:21 pm »
Hi,
Reading the AoE, I never stop to be puzzled by my lack of understanding.

A common emitter amplifier with a gain of 50 and bypassed emitter resistor is presented (page 97, fig 2.50), also:
967766-0
Its requirements are a quiescent current of 1mA and to operate between 20Hz and 20kHz
The text proceeds indicating many things that I don't understand.

First it says that the bypassing capacitor value has been chosen to be small than re (the intrinsic emitter resistance) at the lowest signal frequency. re should be around 25 \$\Omega\$ due to the 1mA collector current.
But calculating Xc= 1/(2pi f C)= 1/(2*pi*20*68*10-6)=106*1/8545≈117 \$\Omega\$ which is way bigger than re. Where am I wrong?

Second it says that the gain is set by the first emitter resistor (180 \$\Omega\$) plus re. Why is that so? I don't understand why the 820 \$\Omega\$ paralleled with the capacity does not count (although it counts for the quiescent current).

Third it's fig 2.51 (which is also in the attachment above). I understand that only the 1k resistor will set the quiescent current; I appreciate that the bypassing side will prevail at signal frequencies, but I cannot understand how this can be equivalent to the circuit before.

Any help is appreciated, I passed the last hour and half trying to understand this with no luck  :(
 

Offline Paul Rose

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Re: Bypassed emitter on Common Emitter Amplifier
« Reply #1 on: April 11, 2020, 03:33:44 pm »
I have the older edition, but it has the same example.

The text there says "the emitter bypass capacitor is chosen to have low impedance compared with 180+25 ohms at the lowest signal frequencies".

Your 117 ohm calculation for 68uF at 20Hz is correct, but it is small compared to 205 (180+25).  Consider that the 68uF cap impedance is already down to 23.5 ohms at 100Hz, and don't be too picky about a gain of exactly 50 at 20Hz.

For your second question, gain is set by 180 + re.    This is because at signal frequency, the 820 ohms is paralleled by the 68uF cap.  At the lowest signal frequency, this will reduce the gain somewhat (down to 35 if I did it right).  Over most of the frequency range, the 820 will be practically shorted by the 68uF cap.

Also consider that the lowest gain of 35 at 20Hz is 70% of the target gain of 50.  This is probably no coincidence, because a voltage ratio of 0.7 is very close to 3db, which is often the value used to measure the usable range of an amplifier.

The quiescent is determined at DC.  The cap is "open" at DC, so the 1k = 820+180 is used.

 
« Last Edit: April 11, 2020, 03:46:05 pm by Paul Rose »
 
The following users thanked this post: rstofer, Moriambar

Offline Moriambar

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Re: Bypassed emitter on Common Emitter Amplifier
« Reply #2 on: April 11, 2020, 05:29:29 pm »
I have the older edition, but it has the same example.

The text there says "the emitter bypass capacitor is chosen to have low impedance compared with 180+25 ohms at the lowest signal frequencies".

Your 117 ohm calculation for 68uF at 20Hz is correct, but it is small compared to 205 (180+25).  Consider that the 68uF cap impedance is already down to 23.5 ohms at 100Hz, and don't be too picky about a gain of exactly 50 at 20Hz.

For your second question, gain is set by 180 + re.    This is because at signal frequency, the 820 ohms is paralleled by the 68uF cap.  At the lowest signal frequency, this will reduce the gain somewhat (down to 35 if I did it right).  Over most of the frequency range, the 820 will be practically shorted by the 68uF cap.

Also consider that the lowest gain of 35 at 20Hz is 70% of the target gain of 50.  This is probably no coincidence, because a voltage ratio of 0.7 is very close to 3db, which is often the value used to measure the usable range of an amplifier.

The quiescent is determined at DC.  The cap is "open" at DC, so the 1k = 820+180 is used.

you are right. I don't know what my brain was reading.
thanks
 


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