Try read this
https://electronics.stackexchange.c...-about-the-meaning-of-re-and-rπ/367430#367430

Do you know now how to do it?

 

Try read this
https://electronics.stackexchange.com/questions/367321/confusion-about-the-meaning-of-re-and-rπ/367430#367430

Do you know now how to do it?

I am sorry but I am totally confused. My calculations were based on a video
and I guess that approach wasn't the same or it was in error.

 

I am sorry but I am totally confused.

Which part you do not understand?

You have assumed hie = 3kΩ and β = 100.

Now convert this hie ≈ r_pi into r'e.

Can you do it?

My calculations were based on a video
and I guess that approach wasn't the same or it was in error

Your circuit is slightly different and this is why you cannot follow the video approach fully.

 

Which part you do not understand?

You have assumed hie = 3kΩ and β = 100.

Now convert this hie ≈ r_pi into r'e.

Can you do it?

IE1 ≈ IC1 = 1 mA
r'e1 = 25mV / IE1 = 25mV / 1 mA = 25Ω

rπ1 = (hfe1 + 1) * re1 = (100 + 1) * 50Ω = 5.05KΩ




Your circuit is slightly different and this is why you cannot follow the video approach fully.

 

IE1 ≈ IC1 = 1 mA
r'e1 = 25mV / IE1 = 25mV / 1 mA = 25Ω

rπ1 = (hfe1 + 1) * re1 = (100 + 1) * 50Ω = 5.05KΩ

Good job. But I see a slip of the pen ( in red).

It shood be:
rπ1 = (hfe1 + 1) * re1 = (100 + 1) *25Ω ≈ 2.5kΩ

And now you should be able to calculate the gain in your amplifier.


As a side note for a hie = 3kΩ we have Ib = 25mV/3kΩ = 8.3μA therefore Ic = 100*8.3μA = 0.833mA

 

Good job. But I see a slip of the pen ( in red).

It shood be:
rπ1 = (hfe1 + 1) * re1 = (100 + 1) *25Ω ≈ 2.5kΩ

And now you should be able to calculate the gain in your amplifier.


As a side note for a hie = 3kΩ we have Ib = 25mV/3kΩ = 8.3μA therefore Ic = 100*8.3μA = 0.833mA

Hi Jony:

Here is my attempt to calculate ACL, AOL, Rin and Ro.
Assumption: 2N3904's hie = 3KΩ and hfe = 100
IC = IE ≈ 1.1mA

r'e = 25mV / IE = 25mV / 1.1mA = 22.73Ω

rπ = hfe * r'e = 100 * 22.73Ω = 2.273KΩ

RL'1 = RC1║RB21║RB22║hie = 3.6K║10K║2.2K║3K = 2.65K║2.2K║3K = 1.2K║3K = 0.857K
RL'2 = RC2║(RF + RE11_2) = 3.6K║18.05K = 3KΩ

Av1 = - hfe * RL'1 / (hie + rπ) = -100 * 0.857K / (3K + 2.273K) = -16.25
Av2 = - hfe * RL'2 / (hie + rπ) = -100 * 3K / (3K + 2.273K) = -43.99

AOL = Av = Av1 * Av2 = -16.25 * -43.99 = 714.84

β = RE11 / RE11 + RF = 50Ω / 50Ω + 18KΩ = 0.00277

AOL * β = 714.84 * 0.00277 = 1.98

ACL = AOL / (1 + (AOL * β)) = 714.84 / (1 + 1.98) = 239.88

Ro = RC║RF = 3.6K║18K = 3KΩ

Ro(Feedback) = Ro / (1 + (AOL * β)) = 3K / (1 + 1.98) = 1.01KΩ

Rin = hie = 3K

Rin(Feedback) = Rin * (1 + (AOL * β)) = 3K * (1 + 1.98) = 8.91KΩ

However, per my sim, ACL = vout / vin = 198.16mV / 1mV = 198

Newbie2019

 

Wrong again. Where is Re11 and Re21 in your equation? And why do you think that hie is not the same as an rπ?

What the hie is to you (also known as an h11 and r_pi )?

 

Wrong again. Where is Re11 and Re21 in your equation? And why do you think that hie is not the same as an rπ?

What the hie is to you (also known as an h11 and r_pi )?

I have never seen any of these before. They were never mentioned in class.

 

So what small-signal model you have been taught in the class room?

 

So what small-signal model you have been taught in the class room?

π model and T model, directly out of the Malvino text.

 

So, stick to the models you know. And calculate voltage gain for each individual stages (you've got all the information you need).

 

Look good. But you have changed the schematic hence the secend stage voltage gain is no longer equal to Av2 = rc2 / (re2 + r'e2) = 36.55

 

Revised Schematic and accompanying AC Analysis.

My calculated ACL is 289 while the sim says 285. I assume that my ACL calculation is therefore correct.

However, I don't think that AOL or Rin after feedback and Rout after feedback is correct.

GENERAL
VCC = 10.00 Volts
rs1 = 0.00 Ω
vs1 = 1.00 mV
f = 20.00 Hz
Vt = 25.00 mV
VBE = 0.70 Volts

COMPONENTS - STAGE 2
RB21 = 10.00 KΩ
RB22 = 2.20 KΩ
RC2 = 3.60 KΩ
RE2 = 1.00 KΩ
RF1 = 18.00 KΩ
RL2 = 10.00 KΩ
Q2 = 2N3904 NPN
Q2 Bdc2 (Min) = Bac2 (Min) 100

COMPONENTS - STAGE 1
RB11 = 10.00 KΩ
RB12 = 2.20 KΩ
RC1 = 3.60 KΩ
RF2 = 0.05 KΩ
RE1 = 0.95 KΩ
Q1 = 2N3904 NPN
Q1 Bdc1 (Min) = Bac1 (Min) 100

DC RESPONSES - STAGE 2
RB21║RB22 = 1.80 KΩ
0.01 * βdc2 * RE2 = 1.00 KΩ
Stiff voltage divider: RB21║RB22 < 0.01 * βdc2 * RE2 Not A Stiff Voltage Source
VB2 = RB22 / (RB21 + RB22) * VCC = 1.80 Volts
VE2 = VB2 - VBE = 1.10 Volts
Estimated IE2 = (VB2 - VBE) / [RE2 + (RB21║RB22) / βdc2] = 1.081 mA
Estimated IC2 ≈ IE2 = 1.081 mA
Estimated IB2 = IC2 / βdc2 = 0.011 mA = 10.81 µA
IE2 = (βdc2 + 1) * IB2 = 1.111 mA

DC RESPONSES - STAGE 1
RB11║RB12 = 1.80 KΩ
0.01 * βdc1 * (RF2 + RE1) = 1.00 KΩ
Stiff voltage divider: RB11║RB12 < 0.01 * βdc1 * (RF2 + RE1) Not A Stiff Voltage Source
VB1 = RB12 / (RB11 + RB12) * VCC = 1.80 Volts
VE1 = VB1 - VBE = 1.10 Volts
Estimated IE1 = (VB1 - VBE) / [RE1 + (RF2 /1000) + (RB11║RB12) / βdc1] = 1.135 mA
Estimated IC1 ≈ IE1 = 1.135 mA
Estimated IB1 = IC1 / βdc1 = 0.011 mA = 1.35 µA
IE1 = (βdc1 + 1) * IB1 = 1.111 mA

AC RESPONSES - STAGE 2
RC2║RL2 = 2.65 KΩ
rc2 = RC2║RL2║RF1 = 2.31 KΩ
re2 = RF2 = 0.05 KΩ
r'e2 = 25mV / IE2 = 22.5 Ω
Rin2(Base) = βac2 * (re2 + r'e2) = .25 KΩ
Rin2(Stage) = RB21║RB22 ║Rin2(Base) = 1.44 KΩ
Rout2 = RC2 = 3.60 KΩ
Av2 = rc2 / r'e2 = 102.67
vin2 = Rin2(Stage) / (Rin2(Stage) + Rout1) * vout1 = 14.17 mV
vout2 = vin2 * Av2 = 1454.83 mV

AC RESPONSES - STAGE 1
rc1 = RC1║Rin2(Stage) = 1.03 KΩ
re1 = RF2 = 0.05 KΩ
r'e1 = 25mV / IE1 = 22.5 Ω
Rin1(Base) = βac1 * (re1 + r'e1) = 7.25 KΩ
Rin1(Stage) = RB11║RB12 ║Rin1(Base) = 1.44 KΩ
Rout1 = RC1 = 3.60 KΩ
Av1 = rc1 / (re1 + r'e1) = 14.21
vin1 = Rin1(Stage) / (Rin1(Stage) + rs1) * vs1 = 1.00 mV
vout1 = vin1 * Av1 = 14.21 mV

AC RESPONSES - AMPLIFIER BEFORE ADDING FEEDBACK
Rin = Rin1 = 1.44 KΩ
Rout = Rout2 = 3.60 KΩ
AOL = Av = Av1 * Av2 = 1458.94
Vin = Vin1 = 1.00 mV
Vout = Vout2 = 1454.83 mV

AC RESPONSES - AMPLIFIER AFTER FEEDBACK ADDED
β = RF2 / RF1 + RF2 = 0.002770
1 + (AOL * β) = 5.04
ACL = AOL / (1 + (AOL * β)) = 289.47
Vout = Vin * ACL = 289.47 mV

Rin' = Rin * (1 + (AOL * β)) = 7.26 KΩ

Rout' = Rout / (1 + (AOL * β)) = 0.71 KΩ

 

newbie2019, if you would post an image of the schematic as well as the asc file, those of us who don't use LTSpice could also see what you're doing.

Also, what does your calculation get for Rin' (Rin with feedback)?
What does LTSpice get for Rin'?

 

Revised Schematic and accompanying AC Analysis.

My calculated AOL is 1459 while the sim value is 1560. Is that correct?

My calculated ACL is 289 while the sim says 285. I assume that my ACL calculation is therefore correct.

However, I don't think that Rin and Rout after adding negative feedback is correct.

GENERAL
VCC = 10.00 Volts
rs1 = 0.00 Ω
vs1 = 1.00 mV
f = 20.00 Hz
Vt = 25.00 mV
VBE = 0.70 Volts

COMPONENTS - STAGE 2
RB21 = 10.00 KΩ
RB22 = 2.20 KΩ
RC2 = 3.60 KΩ
RE2 = 1.00 KΩ
RF1 = 18.00 KΩ
RL2 = 10.00 KΩ
Q2 = 2N3904 NPN
Q2 Bdc2 (Min) = Bac2 (Min) 100

COMPONENTS - STAGE 1
RB11 = 10.00 KΩ
RB12 = 2.20 KΩ
RC1 = 3.60 KΩ
RF2 = 0.05 KΩ
RE1 = 0.95 KΩ
Q1 = 2N3904 NPN
Q1 Bdc1 (Min) = Bac1 (Min) 100

DC RESPONSES - STAGE 2
RB21║RB22 = 1.80 KΩ
0.01 * βdc2 * RE2 = 1.00 KΩ
Stiff voltage divider: RB21║RB22 < 0.01 * βdc2 * RE2 Not A Stiff Voltage Source
VB2 = RB22 / (RB21 + RB22) * VCC = 1.80 Volts
VE2 = VB2 - VBE = 1.10 Volts
Estimated IE2 = (VB2 - VBE) / [RE2 + (RB21║RB22) / βdc2] = 1.081 mA
Estimated IC2 ≈ IE2 = 1.081 mA
Estimated IB2 = IC2 / βdc2 = 0.011 mA = 10.81 µA
IE2 = (βdc2 + 1) * IB2= 1.111 mA

DC RESPONSES - STAGE 1
RB11║RB12 = 1.80 KΩ
0.01 * βdc1 * (RF2 + RE1) = 1.00 KΩ
Stiff voltage divider: RB11║RB12 < 0.01 * βdc1 * (RF2 + RE1) Not A Stiff Voltage Source
VB1 = RB12 / (RB11 + RB12) * VCC = 1.80 Volts
VE1 = VB1 - VBE = 1.10 Volts
Estimated IE1 = (VB1 - VBE) / [RE1 + (RF2 /1000) + (RB11║RB12) / βdc1] = 1.135 mA
Estimated IC1 ≈ IE1 = 1.135 mA
Estimated IB1 = IC1 / βdc1 = 0.011 mA = 1.35 µA
IE1 = (βdc1 + 1) * IB1 1.111 mA

AC RESPONSES - STAGE 2
RC2║RL2 = 2.65 KΩ
rc2 = RC2║RL2║RF1 = 2.31 KΩ
re2 = RF2 = 0.05 KΩ
r'e2 = 25mV / IE2 = 22.5 Ω
Rin2(Base) = βac2 * (re2 + r'e2) = .25 KΩ
Rin2(Stage) = RB21║RB22 ║Rin2(Base) = 1.44 KΩ
Rout2 = RC2 = 3.60 KΩ
Av2 = rc2 / r'e2 = 102.67
vin2 = Rin2(Stage) / (Rin2(Stage) + Rout1) * vout1 = 14.17 mV
vout2 = vin2 * Av2 = 1454.83 mV

AC RESPONSES - STAGE 1
rc1 = RC1║Rin2(Stage) = 1.03 KΩ
re1 = RF2 = 0.05 KΩ
r'e1 = 25mV / IE1 = 22.5 Ω
Rin1(Base) = βac1 * (re1 + r'e1) = 7.25 KΩ
Rin1(Stage) = RB11║RB12 ║Rin1(Base) = 1.44 KΩ
Rout1 = RC1 = 3.60 KΩ
Av1 = rc1 / (re1 + r'e1) = 14.21
vin1 = Rin1(Stage) / (Rin1(Stage) + rs1) * vs1 = 1.00 mV
vout1 = vin1 * Av1 = 14.21 mV

AC RESPONSES - AMPLIFIER BEFORE ADDING FEEDBACK
Rin = Rin1 = 1.44 KΩ
Rout = Rout2 = 3.60 KΩ
AOL = Av = Av1 * Av2 = 1458.94
Vin = Vin1 = 1.00 mV
Vout = Vout2 = 1454.83 mV

AC RESPONSES - AMPLIFIER AFTER FEEDBACK ADDED
β = RF2 / RF1 + RF2 = 0.002770
1 + (AOL * β)= 5.04
ACL = AOL / (1 + (AOL * β)) = 289.47
Vout = Vin * ACL = 289.47 mV

Rin' = Rin * (1 + (AOL * β)) = 7.26 KΩ

Rout' = Rout / (1 + (AOL * β)) = 0.71 KΩ

"
My calculated ACL is 289 while the sim says 285. I assume that my ACL calculation is therefore correct."

lol..It seems you were complaining days ago of your sim not matching precisely with spice
How are you able to tell the gain with spice?

Also, would it make a difference by increasing Rb21 and Rb22?

 

.

 

I don't think that AOL or Rin after feedback and Rout after feedback is correct.

I see an error in Rin. Negative feedback will only increase Rin(base) by a factor of a loop gain.
So for your amplifier Rin is set mainly by RB11 and RB12 resistors value (Rin ≈ 1.8kΩ).

How are you able to tell the gain with spice?

You can use an AC analysis (.ac oct 100 1 10000k) and set the input AC source as 1V. And using a cursors read the voltage gain directly.




Or do the AC analysis for a single frequency only (.ac oct 1 1k 1k) and red the voltage at the output.

 

Hi, Jony130,

What does your spice analysis give for Rout' (Rout with feedback), assuming the input is driven by an ideal voltage source?

 

Hi, Jony130,

What does your spice analysis give for Rout' (Rout with feedback)?

Around 620Ω for a simplified BJT model (β = 100, without early effect) and 493Ω (Va = 100V and β = 311) with a more accurate model.

Without the negative feedback Rout ≈ Rc2||RF ≈ 3kΩ

 

I see an error in Rin. Negative feedback will only increase Rin(base) by a factor of a loop gain.
So for your amplifier Rin is set mainly by RB11 and RB12 resistors value (Rin ≈ 1.8kΩ).


You can use an AC analysis (.ac oct 100 1 10000k) and set the input AC source as 1V. And using a cursors read the voltage gain directly.

View attachment 179154


Or do the AC analysis for a single frequency only (.ac oct 1 1k 1k) and red the voltage at the output.

View attachment 179155

Thanks again, Jony, for your great help. I corrected my Rin(Feedback). Is my ACL = 289 correct then?

I have two points that I need to get clarified.

1) My calculation for AOL = 1458 but the sim shows AOL = vout / vin = 1.56 V / 1 mV = 1560.
I don't understand why the difference?

2) My calculation for Rout(Feedback) = Rout / (1 + (AOL * β)) = 600Ω. Is this correct?

newbie2019