Electronic – If there exists a cascade of op amps, does the previous op amp’s slew rate affect the later op amp’s slew rates

analogcircuitsnon-linearoperational-amplifierslew-rate

All op amps used are the same Texas Instrument LM348n. The datasheet says the op amp has a nominal slew rate of 0.5 V/µs, but gives no tolerance.

I have a square signal with an amplitude of 500 mV peak to peak being sent into a two op amps system. The first op amps is a unity gain op amp. It exists to prevent the wave generator's output impedance from affecting the second op amp's gain. The second op amp is a simple inverting op amp with a gain of -10.

When I measured the slew rate of the inverting op amp alone, I found a slew rate of 0.62 V/µs. However when the cascade circuit is created, the slew rate measured at the second op amp's output is now 0.589 V/µs.

Is this decrease in slew rate due to the fact that the signal was sent through two op amps, each with its own slewing effect? Do the slew rates combine in some way?

Lastly when I set the second op amp to a gain of -1, the slew rate decreases even more to 0.414 V/µs. Is unity gain instability the reason for the second decrease in slew rate?

I thought the slew rate was an intrinsic property of an op amp. Is there a variable that affects slew rate I am not considering?enter image description here

Best Answer

Inspired by the many correct considerations of Tony Stewart, I'll give my contribution and answer in the same order to your questions.

Is this decrease in slew rate due to the fact that the signal was sent through two op amps, each with its own slewing effect?

  • Yes: cascading many stages of amplification lowers the overall speed of their response. Therefore if, for a given input signal step, you get the same output by using a two-stage amplifier instead of a single stage one, you slow down the output signal by rising its rise time \$t_{r_o}\$, and thus the slew rate of the output, defined as $$ \mathrm{SR} = \max\left(\left|\frac{dv_\mathrm{out}(t)}{dt}\right|\right) $$

    Have a look at the Wikipedia entry on rise time, precisely the section on cascaded blocks, for more infos.

Do the slew rates combine in some way?

  • Yes, they combine precisely via the respective output rise times \$t_{R_1}\$ and \$t_{R_2}\$ of their stages (in the presently analyzed two stage amplifier). Roughly speaking, by using the expression for the rise time of the output of cascaded stages found in the reference given above, we get $$ \mathrm{SR}_1\approx \frac{V_{o_{pk}}}{\sqrt{t_{r_i}^2+t_{r_{o1}}^2}} $$ for the single inverting gain stage, and $$ \mathrm{SR}_2\approx \frac{V_{o_{pk}}}{\sqrt{t_{r_i}^2+t_{r_{o2}}^2}} $$ for the single inverting output stage, where

    • \$t_{r_i}\$ is the rise time of the input signal, and
    • \$V_{o_{pk}}\$ is the peak-to-peak maximum output voltage

    When the two stages are cascaded, we obtain roughly $$ \mathrm{SR}\approx \frac{V_{o_{pk}}}{\sqrt{t_{r_i}^2+t_{r_{o1}}^2+t_{r_{o2}}^2}} $$ and thus \$\mathrm{SR}<\mathrm{SR}_1\$, \$\mathrm{SR}<\mathrm{SR}_2\$

Is unity gain instability the reason for the second decrease in slew rate?

  • No, as long as this instability does not affect the rise time of a given stage of the chain, and I suspect it is exactly this that happens when you change the gain of the second stage by rising \$R_2\$ to \$10\mathrm{k}\Omega\$ instead of lowering \$R_1\$ to \$1\mathrm{k}\Omega\$ (given the charateristics of the LM324, perhaps \$R_1=R_2=2\mathrm{k}\Omega\$ would be the best choice, see the discussion at the next point or Tony Stewart's answer). I have not tried to analyze your circuit according to the standard theory, but I suspect that rising \$R_2\$ rises the rise time of the second stage, thus giving you the sensible drop of slew rate you noticed.

I thought the slew rate was an intrinsic property of an op amp. Is there a variable that affects slew rate I am not considering?

  • Yes: slew rate is an intrinsic property of every operational amplifier in the sense that it is the best performance you can get from it. Loading effects, as those explained by Tony Stewart, parasitics and design choices not aimed at obtaining the highest speed of response can and will give you a lower effective slew rate.