One of my readers posted the following questions in the comment section of.I am doing a work on fully differential Negative feedback op-amp with capacitive divider configuration. I have some questions and confusions, can you please clarify?What is the difference between closed loop gain and open loop gain, and are they dependent to each other?How can we calculate the unity gain frequency if I have a 3-dB frequency of 100Hz and closed loop gain of 40dB?Does the feedback factor (BETA) has importance with respect to any other parameters? How will it help in finding the closed transfer function of the system assuming the op-amp as a single pole system?The answers needed some space, more than the comment section could offer, so here is a post on the topics of op amp open-loop, closed-loop and feedback.Q1: What is the difference between closed loop gain and open loop gain, and are they dependent to each other?A1: In general terms, an amplifier in has gain, which represents the ratio between the output signal amplitude versus the input signal amplitude. If the gain is frequency dependent, we note it with A(ω) to show that dependence.
![Closed loop transfer function examples Closed loop transfer function examples](/uploads/1/2/5/4/125465466/239814050.png)
The general architecture of a closed- loop control system is shown in Figure 1, where the key idea is that information from the plant is sensed, and used in computing the signal to send to the actuator.
![Function Function](http://www.expertsmind.com/CMSImages/1630_Obtain%20the%20closed%20loop%20transfer%20function.png)
Figure 1 shows the amplifier, represented as a black-box, with two input signals, V1 and V2, and an output signal Vo. The signals are shown with respect to ground.Figure 1This is the basic op amp. The output Vo depends on the difference between the two inputs as follows:(1)If we bring negative feedback from output to input around this amplifier, in other words, close the loop, the entire system gain changes and its value depends on feedback. As such, we call A(ω) open-loop gain, and the gain of the op amp with negative feedback, closed-loop gain, noted ACL(ω).
Figure 2 shows the block diagram of an amplifier with negative feedback, where the F box shows the feedback network.Figure 2When the loop is closed, equation (1) becomes(2)F is called the feedback coefficient. ACL(ω) depends on A(ω) with the following formula:(3)Of course, F can be dependent on frequency as well, but I want to keep this simple for now. Note: If you want to know how this formula can be derived, here are a few quick steps:(4)Q2: How can we calculate the unity gain frequency if I have a 3-dB frequency of 100Hz and closed loop gain of 40dB?A2: Compensated op amps have one pole. The gain drops at 20 dB per decade after that pole. (see Figure 3).Figure 3In a closed loop system, the gain is set by the feedback network, provided that the open loop gain is high (see answer 3 as well). No matter the closed loop gain level, the product between gain and bandwidth, or the gain bandwidth product (GBW) is constant. Therefore, the GBW in this case is(5)We can apply this value to calculate the unity gain frequency:(6)Q3: Does the feedback factor (BETA) has importance with respect to any other parameters?A3: Yes it does.
The first answer shows that the feedback factor is used in the closed loop gain calculation. Also, if the open loop gain is high, the feedback factor determines the closed loop gain at DC and in band. Indeed, let’s show this by rewriting equation (3) at DC.(7)where with A CLO I noted the closed loop gain and with Ao the open loop gain, both at DC. If Ao is high enough so that 1 in the denominator can be neglected, A CLO becomes(8)Besides determining the gain, if F depends on frequency, it will also modify the amplifier bandwidth. Active analog filters can be designed by simply designing the correct feedback network.Q4: How will it help in finding the closed transfer function of the system assuming the op-amp as a single pole system?A4: The answer to this question is given by equation (3). Eric, this sounds like homework, so all I can do for you is to tell you how to approach this problem, not to solve it for you.
You need to solve it yourself.First of all, you should verify the drop rate between each frequency. Simply calculate the slope.
I calculated that between 0.7 MHz and 3 MHz you have 20 dB/decade, and between 3 MHz and 18 MHz there is 40 dB/decade. You need to prove that before going further.