Summing/Differential Amplifier?

[reno_0405]

I have a question regarding a cascading OpAmp of 1 inverting to a summing? amplifier, the input V1 is 150mV and V2 is 60mV, i know how to calculate without the +0.5V at the Summing + input,
Vo1 = (-Rf/R)Vin = (-120K/47K)V2 for 1st stage,
then Vo2 = (-Rf/R1)V2 - (Rf/R2)V1 = (-33K/10K)Vo1-(33K/22K)V1 = 0.28V
but when applying +0.5V at the Summing + input, my multisim simulation get 3.188V.
can someone show me the formula including the 0.5V input?

**broken link removed**

 

[HATHA]

Hi
if the op amp is ideal one then output is -2.179v

 

[reno_0405]

Hi
if the op amp is ideal one then output is -2.179v

I get positive value 3.18V from simulation.

 

[ericgibbs]

I get positive value 3.18V from simulation.

hi reno,
Whats the supply voltages to the 741 power rails.?

 

[HATHA]

out put voltage of 1st op amp is -v2*120/47= -0.53v

if the op amp are ideal no current drawn in to op amp so voltage at (-)input of op amp2 must 0.5v
though total current through 33k resistor is {(v1-0.5)/22k}+{(-.53-0.5)/10k} =-1.184e-4 A


so (0.5-vo)/33k=-1.184e-4

ooops vo should positive sorry!!!!!!!!!!!!!
vo=0.5+(33k*1.184e-4)=4.4072v

when model ua741 some leakage current may introduce to spice model. and the resister value may tolerate ( most often 5%) though the output may have 3.188v when simulate

 

[ericgibbs]

hi reno.

I have a question regarding a cascading OpAmp of 1 inverting to a summing? amplifier, the input V1 is 150mV and V2 is 60mV, i know how to calculate without the +0.5V at the Summing + input,
Vo1 = (-Rf/R)Vin = (-120K/47K)V2 for 1st stage,

Vo1 = 0.06 * [120/47] = -153mV


then Vo2 = (-Rf/R1)V2 - (Rf/R2)V1 = (-33K/10K)Vo1-(33K/22K)V1 = 0.28V

Vo2[for V1] = 0.15 * [33/22] = -0.225mV

Vo2[for V2o] = -0.153 * [33/10] = +0.504mV

Vo2[for +5Vni] = 0.5( 1 + 3.3] = +2.15V

Algebraic sum of these values =+2.15 + 0.504 - 0.225 = +2.429V

but when applying +0.5V at the Summing + input, my multisim simulation get 3.188V.
can someone show me the formula including the 0.5V input?

Look at this gif.


EDIT: reposted.
NOTE: the non inverting gain is 1+[Rf/Ri]

EDIT: this post has an error.. corrected in a later post.

 

[ericgibbs]

out put voltage of 1st op amp is -v2*120/47= -0.53v

if the op amp are ideal no current drawn in to op amp so voltage at (-)input of op amp2 must 0.5v
though total current through 33k resistor is {(v1-0.5)/22k}+{(-.53-0.5)/10k} =-1.184e-4 A


so (0.5-vo)/33k=-1.184e-4

ooops vo should positive sorry!!!!!!!!!!!!!
vo=0.5+(33k*1.184e-4)=4.4072v

when model ua741 some leakage current may introduce to spice model. and the resister value may tolerate ( most often 5%) though the output may have 3.188v when simulate

hi hatha,
I think you have some typing errors in your post.

I prefer to calculate the final voltage output by working out the gain for each circuit path, then add the individual paths to give the final output.

This helps in error location and also if a different input voltage is applied.

 

[HATHA]

hi eric

I think you have some typing errors in your post.

if so can you show me

-1.184e-4

mean -1.184 *10^(-4) so sorry if it miss understood
actually i thought -1.184E-4
big difference between simple "e" and capital "E" isn't it!!

 

[ericgibbs]

out put voltage of 1st op amp is -v2*120/47= -0.53v

hi,
Just here. V2 = +60mV

 

[Roff]

hi reno.


Look at this gif.


EDIT: reposted.
NOTE: the non inverting gain is 1+[Rf/Ri]

Eric, in your GIF, did you forget the contribution of the 22k resistor to the noninverting gain of the last stage? This makes the noninverting gain 5.9.
I calculate the output voltage to be 3.1805V.

 

[on1aag]

I think you shouldn't make it too difficult for these kids.

Start with the first opamp:

(60.E-3 . 120) / 47 = -153.19.E-3

For the second opamp I take the 0.5 volt as a reference.

The output from the first opamp becomes:

-153,19.E-3 - 500.E-3 = -653,15.E-3

The 150 mV applied to the 22k resistor becomes:

150.E-3 - 500.E-3 = -350.E-3

I only have to introduce the gain of the second opamp and
the correction for the reference level.

-(-653.19.E-3 . 33) / 10 = 2,155

-(-350.E-3 . 33) / 22 = 525.E-3

And add both results:

2,155 + 525.E-3 = 2,680

This result is correct for the reference level of 0,5 volt.
But I need the result for 0 volt, therefore I have to add
the 0,5 volt of the reference level.

2,680 + 0,5 = 3,18

on1aag.

 

[ericgibbs]

Eric, in your GIF, did you forget the contribution of the 22k resistor to the noninverting gain of the last stage? This makes the noninverting gain 5.9.
I calculate the output voltage to be 3.1805V.

Woops!, silly oversight, must be getting old, thanks Roff.


EDIT:
Corrected my previous post calculations:
hi,

Using the Inverting Summing Amp equations I get the following.

Considering the second Inverting Stage.

Vout = -33K( [+0.15/22K] + [-0.153/10K] )

Vout = - 0.225v + 0.5049v = +0.2799v

For the Non Inverting Stage,

Vout = Vin ( [10K||22K + 33K]/10K||22K]}

Vout = 0.5 ( [6.875K +33K]/6.875K)

Vout = 0.5 [5.8] =2.9v

Summing: +2.9V + 0.2799V = +3.1799V. Which is the same as the Spice Sim result