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Non investing closed loop gain factor

Опубликовано в Cpp investment board logo | Октябрь 2, 2012

non investing closed loop gain factor

ideal amplifier signal gain in the noninverting mode. If AVOL in. Equation 1 and Equation 2 is infinite, the closed-loop gain. We can see from the equation above, that the overall closed-loop gain of a non-inverting amplifier will always be greater but never less than one (unity), it is positive in nature and is. to gain peaking and other non-ideal factors. Figure 1 shows the simplified open-loop gain At this point, the closed-loop gain for non-inverting and. AUSTRALIAN INVESTING BLOGS Flexible with or crash blocking for. Supports XP topic listing. Sign up locked to another tab.

Because G CL is essentially bounded by A , the bandwidth fc gets smaller for a higher gain! Life and circuit design are full of compromise, and gain versus bandwidth is a fine example. Can you extend the bandwidth G CL? Sure, make A larger by increasing its gain or bandwidth. Increase the k by a factor of 10 or so. Or, you can increase the bandwidth by decreasing RP1 or CP1 by a factor of Run a new simulation.

Did your new op amp extend the bandwidth at V 4? G N Noise Gain - the gain defined below. Why the name "noise gain"? Typically, noise is modeled as a voltage source at the positive input of the amplifier. So the non-inverting gain is used to calculate the resulting output. Does the noise gain equation look familiar? It should! Calculating its bandwidth fc, we get. Adjust the gain by varying R2 and R1. You should be able to predict the bandwidth at V 4 for any of your chosen gains.

Why call it this? If we rearrange the above equation, we get. What does this mean? You can't arbitrarily set the gain and bandwidth for a given op amp. Alternatively, if you need a higher bandwidth, then you must choose a lower gain. If you need both higher gain and bandwidth, you're out of luck with this device. You need to pick an op amp with a higher GBP fu on its data sheet.

What about the inverting amplifier? The results are similar with a slight twist. Let's start with it's closed-loop gain equation - significantly different than the non-inverting gain. Similar to the non-inverting amplifier, when A is large, the ideal inverting gain is achieved.

However, as frequency increases and A drops close to the ideal gain, G CL begins to drop. How do we predict this frequency where the gain falls off? Similar to the non-inverting amplifier we calculate. The fc calculation also uses the noise gain. But here's the twist, the noise gain for the inverting amp is the same as the non-inverting amp! A log plot on the Y-Axis can give a better view.

For any gain, G CL should be bounded by A. Does the bandwidth get smaller as you increase gain? Here's a showdown between the two classic amplifiers. The challenge is this: for the same gain, which amplifier has the greater bandwidth? We'll use a voltage gain of 2 for both circuits.

Two important circuits of a typical Op Amp are:. A non-inverting amplifier is an op-amp circuit configuration that produces an amplified output signal and this output signal of the non-inverting op-amp is in-phase with the applied input signal. In other words, a non-inverting amplifier behaves like a voltage follower circuit. A non-inverting amplifier also uses a negative feedback connection, but instead of feeding the entire output signal to the input, only a part of the output signal voltage is fed back as input to the inverting input terminal of the op-amp.

The high input impedance and low output impedance of the non-inverting amplifier make the circuit ideal for impedance buffering applications. From the circuit, it can be seen that the R 2 R f in the above picture and R 1 R 1 in the above picture act as a potential divider for the output voltage and the voltage across resistor R 1 is applied to the inverting input.

When the non-inverting input is connected to the ground, i. Since the inverting input terminal is at ground level, the junction of the resistors R 1 and R 2 must also be at ground level. This implies that the voltage drop across R 1 will be zero.

As a result, the current flowing through R 1 and R 2 must be zero. Thus, there are zero voltage drops across R 2 , and therefore the output voltage is equal to the input voltage, which is 0V. When a positive-going input signal is applied to the non-inverting input terminal, the output voltage will shift to keep the inverting input terminal equal to that of the input voltage applied.

Hence, there will be a feedback voltage developed across resistor R 1 ,. The closed-loop voltage gain of a non-inverting amplifier is determined by the ratio of the resistors R 1 and R 2 used in the circuit. Practically, non-inverting amplifiers will have a resistor in series with the input voltage source, to keep the input current the same at both input terminals. In a non-inverting amplifier, there exists a virtual short between the two input terminals. A virtual short is a short circuit for voltage, but an open-circuit for current.

The virtual short uses two properties of an ideal op-amp:. Although virtual short is an ideal approximation, it gives accurate values when used with heavy negative feedback. As long as the op-amp is operating in the linear region not saturated, positively or negatively , the open-loop voltage gain approaches infinity and a virtual short exists between two input terminals. Because of the virtual short, the inverting input voltage follows the non-inverting input voltage.

If the non-inverting input voltage increases or decreases, the inverting input voltage immediately increases or decreases to the same value. In other words, the gain of a voltage follower circuit is unity. The output of the op-amp is directly connected to the inverting input terminal, and the input voltage is applied at the non-inverting input terminal.

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Connect and share knowledge within a single location that is structured and easy to search. What about the open-loop gain? How does the value of open-loop gain and closed-loop gain affect the performance of op-amp? What is the relationship between open-loop and closed-loop gain of op-amp? Closed loop gain is the gain that results when we apply negative feedback to "tame" the open loop gain. The closed loop gain can be calculated if we know the open loop gain and the amount of feedback what fraction of the output voltage is negatively fed back to the input.

The open-loop gain affects the performance generally like this. Firstly, look at the above formula. Thus the formula reduces to:. With a huge open-loop gain, we can precisely set up gains: as precisely as we care to design and build our feedback circuit.

Okay, so far that's more of an issue of clean math and design convenience. Big open loop gain: closed loop gain is simple. But, practically speaking, small open-loop gains means that you must use less negative feedback to achieve a given gain. If the open loop gain is only 50, then we must use much less negative feedback to get a gain of You can work that out with the formula. We generally want to be able to use as much negative feedback as possible, because this stabilizes the amplifier: it makes the amplifier more linear, gives it a higher input impedance and lower output impedance and so on.

From this perspective, amplifiers with huge open loop gains are good. It is usually better to achieve some necessary closed loop gain with an amplifier that has huge open loop gain, and lots of negative feedback, than to use a lower gain amplifier and less negative feedback or even just an amplifier with no negative feedback which happens to have that gain open loop.

The amp with the most negative feedback will be stable, more linear, and so on. Also note that we don't even have to care how huge the open loop gain is. Is it , or is it ,? It doesn't matter: after a certain gain, the simplified approximate formula applies.

Amplifiers based on high gain and negative feedback are therefore very gain-stable. The gain depends only on the feedback, not on the specific open-loop gain of the amplifier. The open loop gain can vary wildly as long as it stays huge. For instance, suppose that the open loop gain is different at different temperatures.

That does not matter. As long as the feedback circuit is not affected by temperature, the closed-loop gain will be the same. My answer covers the non-inverting as well as the inverting opamp-based amplifier. Because the input voltage is directly applied to the summing junction differential input the classical feedback formula from H.

Black applies:. Because now the input voltage is NOT applied directly to the summing junction diff. EDIT : " How does the value of open-loop gain and closed-loop gain affect the performance of op-amp? D The following answer concerns the availabel bandwidth for the non-inverting amplifier as a function of the open-loop bandwidth Aol real opamp :.

In most cases, we can use a first order lowpass function for the real frequency dependence of the open-loop gain:. Hence, the due to negative feedback the bandwidth wo open-loop gain is enlarged by the factor AoHfb. It can be helpful to think of this in terms of excess gain, that being the difference between open loop and closed loop gains.

For example, if the open-loop gain is , and the closed-loop gain is 10, the difference is 99, or nearly dB. Read this essay if it is not clear how I converted gain to dB. If the closed-loop gain is 1, instead, that barely reduces excess gain, because the difference is still very large. You have to get within a factor of 10 difference in this case to reduce the difference to below 99 dB. The open-loop gain of this example amplifier is so high that we can just call the excess gain dB for all practical purposes.

This excess gain contributes to an improvement in performance parameters. But one must take into account the frequency of operation, as the open loop gain has difference dominant poles and zeros, so if you are operating significantly close to those the explanation becomes less simple.

Also, the concept of open loop gain only applies to voltage feedback, voltage mode amplifiers. Alternatively, if the 2 input terminals regulate to the same voltage, this creates a current of 10uA through R2. Looking at this circuit another way, there is a potential divider from the output back to the inverting input. If the circuit regulates to keep the 2 inputs the same, then.

So there are a number of ways of determining the gain of an op amp. Now, it is always assumed that the two input terminals are at the same voltage ignoring the dc offset voltage. In fact the voltage across the input terminals is made up of two components: the dc offset voltage and a much smaller component that is dependent on the open loop gain of the amplifier and it is this second component that most people ignore which leads to confusion when analysing the op amp at ac.

FIG 2. In the following paragraphs, for the sake of clarity, we will assume that the input offset voltage of the amplifier is zero. The open loop gain of the amplifier is equal to the output voltage divided by the differential voltage across the 2 inputs in FIG 2 this is the voltage at the OUT node divided by the voltage Vdiff. The closed loop gain is equal to the voltage at the OUT node divided by the voltage at the IN node, as discussed above.

Regardless of the circuit configuration, the op amp always operates in open loop gain. As circuit designers, we choose to put components around the amplifier to give us a certain closed loop gain , but the amplifier always tries to amplify the voltage Vdiff by its open loop gain to give a voltage at the OUT node. Another way of looking at this is that for any given voltage at the OUT node, there will be a very small voltage, Vdiff, across the input nodes whose magnitude is equal to V OUT divided by the open loop gain.

In op amp theory taught in school, the open loop gain is assumed to be infinite, so the differential voltage, Vdiff is then infinitely small zero. As long as the open loop gain of the amplifier remains high, this voltage is much smaller than the input voltage and can be ignored. However, if the open loop gain of the amplifier goes down, this voltage starts to get bigger and this is discussed below.

The open loop gain is assumed to be infinite and although it is very high at dc, it rolls off soon after DC and this affects the AC performance of the op amp. FIG 3a. The LTspice plot of this is shown in FIG 3b with the solid green line showing the gain and the dotted green line showing the phase. FIG 3b. At frequencies below about 0. Beyond 0. This roll off is exactly the same as a simple RC filter with a cut off frequency at 0.

At low frequencies the voltage Vdiff in FIG 2 will be small due to the high open loop gain of the op amp. However, at higher frequencies above 0. With an input frequency of 0. We can see from FIG 3a that the open loop gain of the amplifier at 0. FIG 4a. In FIG 4b, the frequency is increased to 1Hz and all other circuit parameters remain unchanged.

From FIG 3a, we can see that the open loop gain of the op amp is about dB about , This is slightly easier to see in FIG 3b. The differential voltage, Vdiff, measured across the input is now nV. This corresponds to the output voltage mV divided by the open loop gain at 1Hz , Notice also that in FIG 4a both waveforms are in phase whereas in FIG 4b there is a phase shift between the input and the output.

FIG 4b. In FIG 4c, the frequency is increased to Hz. The open loop gain of the op amp at Hz is 75dB The differential voltage measured across the input is The output voltage is also phase shifted with respect to the input. FIG 4c. Just for completion, changing the feedback resistor in FIG 2 from 9k to 99k gives the amplifier a gain of FIG 4d shows the effect on the output and the differential voltage.

FIG 4d. The output has increased by a factor of 10 as expected , but so has the differential voltage. If the output voltage increases by a factor of 10, for a given open loop gain, this means the differential input voltage also has to increase by a factor of This will have important implications and these will be explained later.

It is interesting to note that although the LT has a very low offset voltage, the simulation model appears to have a virtually zero dc input offset voltage which makes our analysis much easier. Thus it can be seen that the differential input voltage increases with decreasing open loop gain and the output undergoes a phase shift above 0. It should also be noted that, like a simple RC filter, the phase shift occurs at frequencies around the break frequency.

For a single order RC filter one where the gain falls at 20dB per decade the phase shift will only ever get to 90 degrees. FIG 4c shows a phase shift of 90 degrees and if we were to increase the frequency above the Hz shown in FIG 4c, the phase shift would stay at 90 degrees. We can see from FIG 3 that the slope of the open loop gain changes above 1MHz and starts to decay at more than 20dB per decade.

This effect is similar to a second RC filter with a break frequency of 1MHz. This second RC filter will introduce a further 90 degrees phase shift resulting in a degrees phase shift at frequencies well in excess of 1MHz. It is important to remember that although Vdiff is phase shifted with respect to the output, its amplitude is only very small compared to the input voltage of 10mV. The voltage at both input terminals is still approximately 10mV and as long as Vdiff is small compared to the input voltage, we need not worry too much about the phase shift.

Phase Shift. A similar low pass filter this time with a break frequency of 1kHz is shown in FIG 5. FIG 5a. The break frequency occurs when the output is 3dB lower than the input as represented by the solid green line below and read off the left hand axis. FIG 5b. For a single order low pass filter the phase shift at the break frequency is 45 degrees, as represented by the dotted green line above and read off the right hand axis.

As an approximation, for a first order low pass filter, the phase shift at 10x less than the break frequency is about 0 degrees and at 10x greater than the break frequency, the phase shift is 90 degrees and this can be seen in FIG 5b. A mathematical derivation of the amplitude and phase shift can be seen here: Low Pass Filter Amplitude and Phase Shift.

A low pass filter has a phase lag response. This means the output voltage reaches its peak after the input voltage and this can be seen in FIG4c above, although it is not immediately obvious. The voltage at the non inverting input is the forcing function so is at zero phase. The signal passes through the op amp and undergoes a phase lag and this appears at the inverting input. The blue waveform in FIG 4c is measured from the non inverting terminal to the inverting terminal and clearly leads the green waveform.

Therefore if the blue waveform were measured from the inverting terminal to the non inverting terminal it would be lagging the green waveform. FIG 6 shows a similar 2 pole filter with one pole at 1kHz and one at kHz.

It can be seen from FIG 7 that the first pole introduces a roll of at 20 dB per decade and worst case 90 degree phase shift as expected and the second pole introduces a further 20 dB per decade roll off and another 90 degree phase shift.

FIG 6. FIG 7. Some amplifiers, including the LT exhibit an open loop characteristic with 2 break frequencies similar to that in FIG 7. With the LT, the first break frequency is at 0. The open loop phase shift will tend towards degrees as the frequency gets towards 10MHz. Loop Gain. A general feedback system, like most op amp circuits, is represented in FIG 8. FIG 8. It can be seen that. If A 0 is large then the overall closed loop gain approximates to.

This can be seen in FIG 1. The feedback fraction is a simple resistive divider represented by. We are now going to introduce the concept of Loop Gain. It should be noted that loop gain , open loop gain and closed loop gain are 3 different parameters and should not be confused. Loop gain is not something that is measured in everyday electronics, but it is useful in explaining how op amps might start misbehaving at high frequencies. Referring to FIG 2 we know that open loop gain is defined as:.

And closed loop gain is defined as. This is easy to picture in FIG 8. In other words, the loop gain is a measure of how big the input voltage, V IN , is compared with the differential voltage, Vdiff. However, this is only an approximation. To find the exact value of the loop gain, we need to examine FIG 8. We would not normally measure the magnitude of the input voltage and compare it with the differential voltage, so why is this of any use?

From the equation above, this represents a high loop gain. However, if Vdiff starts to become comparable to V IN as loop gain reduces it will start to interfere with the input signal and can no longer be ignored. However, if the op amp has a second order response as shown in FIG 7 then it is possible that the phase of Vdiff can be close to degrees out of phase with the input at high frequencies.

Again this is not normally a problem if Vdiff is small compared with V IN , but if Vdiff is comparable in magnitude with V IN , then we are nearing a point of potential oscillation. Put another way, under normal circumstances the voltage fed back is applied to the inverting input so opposes the input signal.

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