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OPA140: Calculate the amplification of the whole circuit.

Part Number: OPA140
Other Parts Discussed in Thread: TINA-TI, , LMH6645

Hello everyone,

I need help to calculate the gain of the amplifier circuit below.

Thanks,

Hai

  • Hi Lai,

    I would run a TINA-TI simulation. It's free and can be downloaded here:

    http://www.ti.com/tool/TINA-TI

    Kai

  • Hello Hai,

    Running a TINA-TI circuit simulation as Kai suggested would allow you to see what the gain looks like across frequency. It will change with frequency due to the addition of the various RC networks and limited gain-bandwidths of the op amps.

    If you are looking for the dc and low-frequency ac gain it can be determined as follows:

    U1 - Inverting amplifier, G1 = -R2/R1 = 196 k/499 = -392.8 V/V

    U2 - Variable gain non-inverting amplifier, G2min = 1 + VR1min/R5 = +1 V/V, when VR1 = 0 Ohms, and G2max = 1 + VR1max/R5 = 1 + 25 k/1 k = +26 V/V

    U3 - Sallen-key low-pass filter, G3 = 1 + R9/R8 = 1 + 1 k/1 k = +2 V/V

    Gmin = G1 x G2min x G3 = (-392.8 V/V) (+1 V/V) (+2 V/V) = -785.6 V/V

    Gmax = G1 x G2max x G3 = (-392.8 V/V) (+26 V/V) (+2 V/V) = -20,426 V/V

    Therefore, the gain is dependent on the VR1 setting.

    I hope this is what you needed.

    Regards, Thomas

    Precision Amplifiers Applications Engineering

  • Thomas Kuehl said:

    Hello Hai,

    Running a TINA-TI circuit simulation as Kai suggested would allow you to see what the gain looks like across frequency. It will change with frequency due to the addition of the various RC networks and limited gain-bandwidths of the op amps.

    If you are looking for the dc and low-frequency ac gain it can be determined as follows:

    U1 - Inverting amplifier, G1 = -R2/R1 = 196 k/499 = -392.8 V/V

    U2 - Variable gain non-inverting amplifier, G2min = 1 + VR1min/R5 = +1 V/V, when VR1 = 0 Ohms, and G2max = 1 + VR1max/R5 = 1 + 25 k/1 k = +26 V/V

    U3 - Sallen-key low-pass filter, G3 = 1 + R9/R8 = 1 + 1 k/1 k = +2 V/V

    Gmin = G1 x G2min x G3 = (-392.8 V/V) (+1 V/V) (+2 V/V) = -785.6 V/V

    Gmax = G1 x G2max x G3 = (-392.8 V/V) (+26 V/V) (+2 V/V) = -20,426 V/V

    Therefore, the gain is dependent on the VR1 setting.

    I hope this is what you needed.

    Regards, Thomas

    Precision Amplifiers Applications Engineering

    Dear Thomas,

    Thanks for your answer. This is a very detailed answer.
    But I still want to know more about the roles of C2, R3, R4 and C3, C4, C5, R6, R7 and C6.
    Thank you very much.

    Hai

  • kai klaas69 said:

    Hi Lai,

    I would run a TINA-TI simulation. It's free and can be downloaded here:

    http://www.ti.com/tool/TINA-TI

    Kai

    Dear Kai,

    Thanks for your answer.
    I spent time with TINA but it was still too new for me.
    Can you help me set up the simulation?

    Thanks,

    Hai

  • Hi Hai,

    there's a nice training video series showing how to work with TINA-TI:

    Kai

  • Hello Hai,

    Determining the frequency responses contributed by the various components in your application circuit is somewhat outside of the realm of the assistance we provide. It has less to do with the actual OPA140 and LMH6645 op amps and more to do with network analysis.  

    I will provide some general comments about your question, "I still want to know more about the roles of C2, R3, R4 and C3, C4, C5, R6, R7 and C6."

    • C1 shunts R2 and as frequency is increased the capacitive reactance of C1 decreases. This causes the gain to roll of with increased frequency. This introduces a first-order low-pass filter response (-20 dB/dec).
    • R3 and R4 form a voltage divider at the output of U1, and C3 shunts R3. As frequency increases C3's capacitive reactance decreases shunting R3 in the divider. This has the effect of increasing the voltage divider output voltage as frequency is increased, which results in a first-order high-pass response (+20 dB/dec).
    • C4, C5, R6, R7 are the network components associated with a Sallen-Key low-pass filter topology. The circuits produces a second-order low-pass filter response (-40 dB/dec). The math of the second-order stage is reasonably complex and if you need to know more I suggest Googling the Sallen-Key filter topology. There are many good resources that delve into the theory of the filter. 
    • C6 modifies the low-frequency response of the Sallen-Key low-pass filter stage. C6 in conjunction with R8 adds a low-frequency, first-order high-pass response to the filter stage (+20 dB/dec).

    A mathematical analysis of each stage can be accomplished and their math product would reveal the overall frequency response of the complete amplifier. Doing so requires a good understanding of complex circuit analysis, and the effort can be time consuming.

    Kai's suggestion to apply TINA-TI and do a frequency sweep will provide the correct response over frequency and should take less time than attempting a mathematical analysis - even if you have to learn how to use TINA-TI. TINA-TI is very intuitive and easy to learn and Kai has pointed you to online training.

    Regards, Thomas

    Precision Amplifiers Applications Engineering 

  • Dear Thomas,

    Thanks for your support.

    Hai

  • Thomas Kuehl said:

    Hello Hai,

    Determining the frequency responses contributed by the various components in your application circuit is somewhat outside of the realm of the assistance we provide. It has less to do with the actual OPA140 and LMH6645 op amps and more to do with network analysis.  

    I will provide some general comments about your question, "I still want to know more about the roles of C2, R3, R4 and C3, C4, C5, R6, R7 and C6."

    • C1 shunts R2 and as frequency is increased the capacitive reactance of C1 decreases. This causes the gain to roll of with increased frequency. This introduces a first-order low-pass filter response (-20 dB/dec).
    • R3 and R4 form a voltage divider at the output of U1, and C3 shunts R3. As frequency increases C3's capacitive reactance decreases shunting R3 in the divider. This has the effect of increasing the voltage divider output voltage as frequency is increased, which results in a first-order high-pass response (+20 dB/dec).
    • C4, C5, R6, R7 are the network components associated with a Sallen-Key low-pass filter topology. The circuits produces a second-order low-pass filter response (-40 dB/dec). The math of the second-order stage is reasonably complex and if you need to know more I suggest Googling the Sallen-Key filter topology. There are many good resources that delve into the theory of the filter. 
    • C6 modifies the low-frequency response of the Sallen-Key low-pass filter stage. C6 in conjunction with R8 adds a low-frequency, first-order high-pass response to the filter stage (+20 dB/dec).

    A mathematical analysis of each stage can be accomplished and their math product would reveal the overall frequency response of the complete amplifier. Doing so requires a good understanding of complex circuit analysis, and the effort can be time consuming.

    Kai's suggestion to apply TINA-TI and do a frequency sweep will provide the correct response over frequency and should take less time than attempting a mathematical analysis - even if you have to learn how to use TINA-TI. TINA-TI is very intuitive and easy to learn and Kai has pointed you to online training.

    Regards, Thomas

    Precision Amplifiers Applications Engineering 

    Dear Thomas,

    I have set up simulation file for this circuit.8446.amplifier.TSC

    Now I need to analyze what factors, what characteristics of the circuit, to understand how this circuit works?

    Hai,

  • Hi Hai,

    now you can carry out an "AC analysis" and a "transient analysis":

    hai_opa140.TSC

    Kai

  • kai klaas69 said:

    Hi Hai,

    now you can carry out an "AC analysis" and a "transient analysis":

    (Please visit the site to view this file)

    Kai

    Thanks you.

    Hai