Integrated Circuit

An integrated circuit refers to a chip that contains various interconnected multiple electronic components. Furthermore, the location of this chip is on a semiconductor material and it contains both passive and active components. Moreover, the two main types of integrated circuit are- digital integrated circuit and analog integrated circuit.

Introduction to Integrated Circuit

As the components in this type of electronic circuit are not separable and the circuit is integrated on the semiconductor wafer, it is commonly referred to as an Integrated Circuit. Experts also call it as IC as chip or microchip.

Integrated circuit uses have various advantages like low power consumption, lesser weight, compact size, reduced cost, increased reliability, and improved operating speeds. Furthermore, the operational amplifier is a popular integrated circuit. Also, the main parameters of an operational amplifier are open-loop voltage gain, common-mode rejection ratio, and slew rate.

How do we Measure Integrated Circuit?

The measurement of open-loop gain takes place when there is no application of feedback to the op-amp circuit. In other words, it runs in an open-loop format.

In this configuration, the gain figures for the op-amp are normally very high, ranging between 10 000 and 100 000. Most noteworthy, this refers to the gain of the operational amplifier on its own.

There certainly are various ways to measure the common-mode rejection ratio. One of such ways is the four precision resistor method to configure the op-amp as a differential amplifier. Under this method, the application of the signal takes place to both the inputs.

A measurement of the changes in the output takes place.  The inherent difficulties or properties of this particular circuit are that the resistors ratio match is as essential as the CMRR of the op-amp.

There is a mismatch of 0.1% between resistor pair. Furthermore, the result would be in 66 dB CMR. As such, most amplifiers shall operate with a low frequency of CMR that is ranging between the 80dB to 120dB.

When it comes to the slew rate, its governance takes place by factors that are within the operational amplifier chip itself. Accordingly, it is essential to select a chip for the electronic circuit design that would have the required slew rate. Furthermore, calculation of the particular circuit scenario’s required slew rate means that any issues can be dealt at the circuit’s early design stage.

The process of the calculation of the slew rate of an amplifier is relatively easy. Furthermore, this calculation is for an amplifier whose requirement is for a particular electronic circuit design or application. Also, knowledge of the maximum voltage and frequency is very much required for carrying out this calculation.

Formula of Integrated Circuit

Open-loop voltage gain:

The open-loop voltage gain of an op-amp refers to its differential gain excluding any feedback path.

Mathematically, the representation of the open-loop voltage gain of an op-amp can take place as −

A_V = V_O/V₁−V₂

Common-Mode Rejection Ratio:

Common-Mode Rejection Ratio (CMRR) of an op-amp, simply speaking, refers to the ratio of the closed-loop differential gain, A_D and the common-mode gain, A_C.

Mathematically, the representation of CMRR can take place as −

CMRR=A_D/A_C

An important point to note here is that the common-mode gain, A_C, of an op-amp, happens to be the ratio of the common-mode input voltage and the common-mode output voltage.

Slew Rate:

One can define the slew rate of an op-amp as simply the maximum rate of change of the output voltage because of a step input voltage.

Mathematically, the representation of slew rate (SR) can take place as −

SR=Maximum of dV_o/dt

Where V_o refers to the output voltage. In general, the measurement of the slew rate can take place in either V/μSec or V/mSec.

Derivation of the Formula of Integrated Circuit

For resistive feedback: H_FB =R1/R1+R2

A) Non-inverting

Due to the direct application of the input voltage to the summing junction (differential input), there would be the application of the classical feedback formula from H. Black:

A_CL =A_OL/1+H_FB⋅A_OL =1/1/A_OL+H_FB

For A_OL>>H_FB we have

A_CL=1H_FB =1+R2/R1

B) Inverting

Now the application of the input voltage does not take place directly to the summing junction (diff. input pair), rather it takes place through a resistive voltage divider to the inverting terminal. Furthermore, the corresponding reduction of the input voltage takes place before the application of the formula for A_cl. Most importantly, due to the superposition rule, there would be a setting of (assuming V_OUT =0)

H_IN= −R2/R1+R2

Hence we have:

A_CL = H_IN⋅A_OL/1+H_FB⋅A_OL= H_IN/1/A_OL +H_FB

For AOL>>HFBAOL>>HFB we have

A_CL =H_IN/H_FB =−R2/R1+R2/R1/R1+R2 = −R2/R1

C) Final remark: Taking into account that the feedback factor acts back to the negative (inverting) opamp input, the product –H_FB⋅A_OLis referred to as the loop gain.

Common-mode rejection ratio:

However, one can describe the output of a real differential amplifier in a better manner as:

V_O = A_d(V₊ + V_–) + 1/2A_cm(V₊ + V_–)

Where A_cm refers to the common-“mode gain”. The mode gain happens to be significantly smaller in comparison to the differential gain.

One can define the CMRR as the ratio of the powers of the differential gain over the common-mode gain, whose measurement takes place in positive decibels (thereby using the 20 log rule):

CMRR = ( A_d/|A_cm|) = 10log₁₀ ( A_d/A_cm)² dB = 20log₁₀ (A_d/|A_cm|)dB

Slew Rate:

For the purpose of simplicity, let’s assume that the parallel resistance is infinite. Therefore, the current I that enters the load will flow to the capacitor but not to the resistance. Then, one can define the rate of voltage change across the capacitor by the well-known formula:

dV/dt = I/C.

If there is a limitation for the current being sourced to this load (and in reality always is), say at I_max, the maximum voltage change per unit time would be:

SR = max(dV/dt) = I_max/C

Most noteworthy, this is the Slew-Rate.

FAQs on Integrated Circuit

Question 1: What is meant by an integrated circuit?

Answer 1: An integrated circuit is a chip containing various interconnected multiple electronic components. Furthermore, the chip is on a semiconductor material and it has both passive and active components.

Question 2: What are the two main types of integrated circuit?

Answer 2: There certainly are two main types of the integrated circuit. These two types are- analog integrated circuit and digital integrated circuit.