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Nov 22 2019

Core Problems about Operational Amplifier Basics

Intoduction

An operational amplifier, or op-amp for short is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. In this configuration, an op-amp produces an output potential that is typically hundreds of thousands of times larger than the potential difference between its input terminals, and is a voltage amplifying device designed to be used with external feedback components such as resistors and capacitors between its output and input terminals. They are used extensively in signal conditioning, filtering or to perform mathematical operations such as add, subtract, integration and differentiation.

In this video, the basic introduction of the Operational Amplifier (Op-Amp) has been given and different characteristics of ideal and real Op-amp (General Purpose 741 Op-Amp) has been discussed. 


When using op amp, there will be more problems confusing us, what are they? Listing all of them is impossible, but we can seize the core of these problems, which are the following lists.

  • Amplification principle

There are many types of op amps with many functions, and their circuits are inconsistent, but the internal block diagrams are basically the same. It consists of three parts: input stage, intermediate stage, and output stage. The input stage consists of a differential amplifier circuit that uses circuit symmetry to improve overall circuit, and the main function of the intermediate voltage amplifier stage is to increase the voltage gain. It can be composed of one or more stages of amplifying circuits; the output stage has a voltage gain of 1, but can provide a certain amount of power, and the circuit consists of two power supplies V+ and V-.

The entire amplifier circuit is designed with two inputs P and N, and one output O. The voltages of the three terminals are represented by Vp, Vn, and Vo, respectively. The two ends of P and N are respectively called the non-inverting input terminal and the inverting input terminal, which means that when the P terminal is added with the voltage signal Vp (Vn = 0), it is obtained at the output end. The voltage Vo is in-phase with Vp, when the voltage signal Vn (Vp = 0) is applied to the N terminal, the output voltage Vo obtained at the output is inverted from Vp.

The operational amplifier is actually a differential amplifier. Look at its structure, two transistors are connected back to back to share the crossing current source. One of the transistors is the positive input of the op amp and the other is the inverting input. The positive input is amplified and sent to a power amplifier circuit to amplify the output. Thus, if the voltage at the forward input rises, the output naturally becomes larger. If the voltage at the inverting input rises, the reverse current is large, and the forward current is small, because the inverting tertiary tube and the forward tube share a same current source.

Ideal op amp

  •  Balance resistor

Generally, there is a balance resistor in the inverting / non-inverting amplifier circuit. What is the role of this balance resistor?

(1) Provide a suitable static bias for the transistors inside the chip.

The internal circuit of the chip is usually directly coupled, and it can automatically adjust the static operating point, but if an input pin is directly connected to the power supply or the ground, its automatic adjustment function can not work normally. Because the voltage of the ground cannot be raised by the inside transistors, and the voltage of the power supply cannot be reduced, which causes the chip to fail to meet the conditions of virtual short and virtual open.

(2) Eliminate the influence of the static base current on the output voltage, and the value should be balanced with the equivalent resistance value of the external DC of the two input terminals.

(3) In non-inverting op amp circuit, if it not connecting a balance resistor, the op amp will be burned, because the resistor acts as a voltage divider.


  • Feedback resistor in parallel with a capacitor 

What is the role of the feedback resistor in parallel with a capacitor when using non-inverting op amp?

(1) The feedback resistor and capacitor form a high-pass filter, so that local high-frequency amplification is particularly noticeable.

(2) Prevent self-excitation.

 

  • Pulling down resistor and pulling up the capacitor

What role does the role of pulling down resistor and pulling up the capacitor at the input of the op amp play?

To get positive feedback and negative feedback, depending on the specific circuit connection. For example, if the input voltage signal and the output voltage signal are taken to the input, the partial output signal passes through the balance resistor to obtain a new voltage value, that is, shunting the input voltage to make the input voltage smaller, and this is a negative feedback. Since the signal output from the signal source is always constant, the output signal can be corrected by negative feedback.

 

  • Parasitical resistor as an integrator

What is the function of the resistor RF connected to the op amp as an integrator at the two ends of the integrating capacitor?

Adjust resistance to prevent the output voltage from running out of control.

 

  • Parasitical resistors and capacitors

Why are resistors and capacitors connected in series at the input of the op amp?

Regardless of the type of op amp, it consists of transistors or MOS transistors. In the absence of an external components, the op amp is a comparator actually. When the voltage of the non-inverting terminal is high, it will output a level similar to the positive voltage, and vice versa, but this op amp does not seem to have much use. Only when the external circuit is formed to generate the feedback will make the real op amp function.

 

  • Balance resistor failure

What is the consequence of the balance resistor doesn't work well in non-inverting amplifier circuit?

(1) The non-inverting end is unbalanced. For example, there will be an output although the input is 0. When the input signal is output, the output value is always larger (or smaller) than the theoretical output value by a fixed number.

(2) The error caused by the input bias current cannot be eliminated.

 

  • Magnification, input impedence, voltage

What is the amplification factor and input impedence of an ideal integrated operational amplifier? What is the voltage between the non-inverting input and the inverting input?

The magnification is infinite, the input impedance is infinitesimal, and the voltage is almost the same (the voltage is not 0V, for example, the non-inverting end is 10V and the inverting end is 9.99V).


  • Open loop gain

Why is the open loop gain of an ideal op amp infinite?

1) The actual open loop gain of the op amp is very large, so imagine it as infinity and derive the virtual ground from it.

2) Deriving virtual ground is not only an inverting amplifier for the negative feedback connection, because there is no virtual ground for positive feedback.

The open-loop gain of the op amp is infinite, when design the circuit, the closed-loop gain can be independent of the open-loop gain, and only depends on the external components. It is to use the large open loop gain in exchange for the stability of the closed loop gain.

3) Assuming that the gain is small, the difference between the voltages applied across the op amp is relatively large for an output voltage. If it is connected to a negative feedback state, the voltage across the op amp will be different, causing amplification.

We all know that the op amps output voltage Vo is equal to the difference Vid between the non-inverting input voltage and the inverting input voltage, multiplied by the op amps open-loop gain A, that is, Vo = Vid * A = (VI + - VI-) * A ( 1 ). Since the output voltage of the op amp does not exceed the supply voltage in practice, it is a finite value. In this case, if A is large, (VI+ - VI-) is necessarily small; if (VI+ - VI-) is small enough, then we can actually treat it as 0, at this time,  there will be VI+ = VI-, that is, the voltage at the non-inverting input of the op amp is equal to the voltage at the inverting input. This is what we call “virtual short”. Note that they are not really connected together, and there is resistance between them.

In the above discussion, how did we get the result of “virtual short”? Our starting point is the formula (1), which is based on the characteristics of the op amp. Then, we made two important assumptions, one is that the output voltage of the op amp is limited, and it not exceed the power supply voltage; the second is that the open loop gain A of the op amp is large. The A of a normal op amp usually reaches 106 or 107 or even larger, but the actual open loop gain of the op amp is also related to its working state. For example, if the op amp is not working in the linear area, the value A may be small, so second assumption is conditional.

Therefore, we know that when the open loop gain A of the op amp is large, the op amp can have a virtual short. But it is one of the possibilities, and it is not suitable for every op amp in any case to say their inputs are virtual short, in other words, virtual short can only be achieved in circuits under certain conditions.

  • The conditions of virtual short:

a. The open-loop gain of operational amplifier should be large enough.

b. There should be a negative feedback circuit.

 Op-Amp Output

From the above we know when we need to analyze the virtual short in the circuit. In reality, condition (1) is true for most op amps, and the important point is to look at the work area. If it is a circuit drawing, judge by calculation; if it is an actual circuit, it is reasonable to use the instrument to measure amplifier output voltage.

There is also a situation related to virtual short called virtual ground, that is, there is a virtual short when the input is grounded. Some books say that virtual short will be exist under deep negative feedback conditions, but in reality, the op amp is more likely to work in the linear region under this situation. But this is not absolute, when the input signal is too large, the op amp with deep negative feedback will still be saturated. Therefore, it should be judged to be the most reliable with the output voltage value.


  •  Virtual short

Add the input signal directly to the non-inverting input, and the inverting input is grounded through the resistor. Why is U-= U+ = Ui≠0? Is it not a virtual short? What are the conditions that the virtual ground exists?

(1) In the non-inverting amplifier circuit, the output affects by the feedback, so that U(+) automatically tracks U(-), so they will be close to zero. It seems that the two ends are short circuit, so it is called virtual short.

(2) Due to the virtual short phenomenon and the high input resistance of the op amp, the current flowing through the two input terminals is small, approaching 0. This phenomenon is called virtual open, which is derived from virtual short.

(3) The virtual ground is in the inverting op amp circuit, the (+) terminal is grounded, and the (-) is connected to the input and feedback network. Due to the virtual short, U(-) and U(+) are very close, which is said to be virtual ground.

(4) About the conditions: the virtual short is an important feature of the closed-loop (negative feedback) operating state of the non-inverting amplifier circuit; the virtual ground is an important feature of the inverting amplifier circuit in the closed-loop operating state.

 

  • Application

When a operational amplifier is connected as a non-inverting amplifier, the potentials of the two inputs are the same. If the waveform of the input is measured, it will be the same. This is like a common-mode signal. In fact, there are still small differential mode signal on the two inputs, but the differential mode signal can not be measured by the general instrument. As a result, the virtual short artificially increases the common-mode signal at the two inputs, which poses a challenge to the performance of the operational amplifier. Why is an op amp used like this?

(1) The common mode signal of the non-inverting amplifier is much larger than the inverting amplifier, and strict to the common mode rejection ratio.

(2) For single-ended input, the equivalent common-mode value is half of the input value, whether non-inverting or inverting input. However, since the input impedance of the non-inverting amplifier is usually larger than the inverting amplification, the anti-interference ability is a little poor.

As mentioned above, when the inverting input is performed, the voltage at the inverting terminal is almost zero, so the differential influence on the tube collector voltage that has only one tube change. When the input is in phase, the voltage at the inverting terminal is equal to the non-inverting terminal voltage, so the common mode voltage and the input voltage are equivalent. That is to say, the collector voltage of the differential tube has variable quantity that changes in the same direction when the two tubes have portions that change in different directions at the same time, which is the common mode output voltage. It is added in phase with the voltage of one of the tubes. Therefore, it is easy to cause the tube to become saturated (or cut off), fortunately, the amplification of the common mode voltage is only tens of thousands of parts of the differential mode amplification.

However, this does not mean that the common mode rejection suppression ratio of the differential mode input and the common mode input of the amplifier is different. It should be that the non-inverting input is added with a common mode signal equivalent to the input volume, so it should be careful to use non-inverting amplification mode when the input signal is large.

 

  • Sampling

Why is the amplifier circuit composed of operational amplifiers generally sampling the inverting input mode?

(1) The significant difference between the inverting input and the non-inverting input mode is:

When inverting input, because there is a balanced resistor connected to the ground at the same phase, and there is no current on this resistor (because the input resistance of the op amp is extremely large), this non-inverting terminal is approximately equal to the ground potential, and  the potential at the non-inverting terminal is extremely close to the inverting terminal, so there is a virtual ground at the inverting end. The advantage of having a virtual ground is that there is no common mode input signal, even if the common mode rejection ratio is not high, there is no common mode output.

The non-inverting input mode has no virtual ground. When a single-ended input signal is used, a common-mode input signal is generated. Even if an operational amplifier with a high common-mode rejection ratio is used, there is still a common-mode output. Therefore, it is best to use the inverting input method.

(2) The positive phase is the oscillator, and the inverting can stabilize the amplifier and access the negative feedback.

(3) From the principle point of view, it is possible to connect to the same analog circuit. However, the signal (differential mode signal) that is amplified during the actual application tends to be small, thus it is necessary to pay attention to suppressing noise (usually expressed as a common mode signal). In the same way, the amplification circuit has a poor ability to suppress the common mode signal, and the signal that needs to be amplified is submerged in the noise, which is not conducive to post processing. Therefore, an inverting proportional amplification circuit with better suppression capability is good.

Op-Amp Basics

  • Reference voltage

Some op amps will have an output even if no voltage is input after power-on, and the output is not small, so VCC/2 is often used as the reference voltage.

The output is output signal without any input, this is called the input offset voltage Vos, which is caused by the asymmetry of the design structure of the op amp. It is a very important performance indicator of the op amp. The op amp commonly used VCC/2 as the reference voltage is because the op amp is in a single power supply state. At this time, the real reference of the op amp is VCC/2, so a DC offset of VCC/2 is often provided at the positive terminal of the op amp. When having positive and negative dual power supply, it is often referenced to the ground.

The selection of op amps requires attention to many things. Under less stringent conditions, it is often necessary to consider the operating voltage, output current, power consumption, gain bandwidth product, and price of the op amp. Of course, when using it under special conditions, different factors must be considered in practice.

 

  • Importance of Op amp

(1) If the voltage on both inputs of the op amp is 0V, the output voltage should also be equal to 0V. But in fact, there is always some voltage at the output, that is, the offset voltage Vos. If the offset voltage at the output is divided by the noise gain of the circuit, the calculated result is called the input offset voltage or the input reference offset voltage. The Vos is considered to be a voltage source in series with the inverting input of the op amp. A differential voltage must be applied to both inputs of the amplifier to produce a 0V output.

(2) The input impedance of an ideal op amp is infinite, so no current flows into the input. However, a real op amp using a bipolar junction transistor (BJT) in the input stage requires some operating current, which is called bias current (IB). There are usually two bias currents: IB+ and IB-, which flow into the two inputs, respectively. The range of IB values is large, with bias currents of lower at 60fA for special op amps and up to tens of mA for some high-speed op amps.

(3) The power supply voltage range required for the first single-chip op amp to operate normally is ±15V. Today, op amps are moving toward low voltages due to increased circuit speeds and power supplies from low-power sources such as batteries. Although the op amps voltage specifications are usually specified as symmetrical two-pole voltages ±15V, these voltages do not necessarily require a symmetrical voltage or a two-pole voltage. For an op amp, as long as the input is biased in the active region (within the common-mode voltage range), the ±15V supply is equivalent to a +30V/0V supply, or a +20V/-10V supply. The op amp does not have a ground pin unless the negative voltage rail is grounded in a single-supply application.

The input voltage swing of high speed circuits is smaller than that of low speed devices. The higher the speed of the device, the smaller its geometry, which means the lower the breakdown voltage. Due to the low breakdown voltage, the device must operate at a lower supply voltage. Today, op amps typically have a breakdown voltage of around ±7V, so high-speed op amps can work at a supply voltage of ±5V, and they can also operate at a single supply voltage of +5V.

For general-purpose op amps, the supply voltage can be as low as +1~8V. These op amps are powered by a single power supply, but this does not mean that a low supply voltage must be used. Because the terms single supply voltage and low voltage are two related and independent concepts.

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