Hey friends, welcome to the Kohiki Web ALL ABOUT ELECTRONICS. So, in the last article, we have discussed the DC offset errors in the op-amps. In the Previous Article, we discussed Op-Amp: Input Offset Voltage Explained (kohiki.com) And we have seen that usually, the op-amp manufacturers used to provide the three parameters related to these DC offset errors. And out of the three parameters we have already discussed the input offset voltage. So, now in this article, let’s understand the input offset current and the input bias current.

## What is input bias current and input offset current?

let’s see how these currents can affect the output of the op-amp. And how we can reduce the effect of this bias current. So, now so far in our discussion, we have assumed that the op-amp is an ideal op-amp.

That means no current is flowing into the op-amp terminals. But actually, if you see, whenever the biasing voltages are applied to the op-amp, at that time a small amount of current used to flow through these input terminals. And these currents are known as the input bias currents. So, let’s say, the current that is flowing through this non-inverting terminal is IB+, and the current that is flowing through this inverting terminal is IB-.

**Input Bias Current**

So, if you see the internal structure of this op-amp, then these currents are basically the currents that are flowing through these transistors of the differential amplifier. So, if this op-amp is constructed using the bipolar transistors, then these biasing currents are basically the base currents of these transistors. And if op-amp is designed using the MOSFETs or JFET, in that case, these biasing currents are the gate currents of these transistors.

Now, the direction of these biasing currents depends upon the type of transistors that are used in the development of this op-amp. For example, if this differential amplifier is designed using the NPN transistors, in that case, these biasing currents are entering into the op-amp. While, in the case of PNP transistors, these biasing currents are going in the outward direction. Now, usually the datasheets, this input bias current is defined as the average value of these two currents.

So, we can say that the input bias current is the average value of this current IB+ and the IB-.So, that is the definition of the input bias current. Now, ideally, these two biasing currents should be identical. But because of some mismatch between the two transistors, there will be some difference between the two biasing currents. And the difference between the two input bias currents is usually defined as the input offset current in the datasheets.

**Input Offset Current**

So, this input offsets current is the difference between the two biasing currents. Now, this input offsets current can be either positive or negative. But in datasheets, this input offset current is defined by absolute value. Now, for the general purpose op-amps, the value of this input bias current used to be in the range of nano-amperes.

But it can be as high as micro-ampers for very high-speed op-amps. Or it can be as low as femtoamperes for very precise amplifiers. For example, if you take the case of LT6273, which is a very high-speed op-amp, that case the value of this input bias current used to be in the range of micro-amperes.

**Input Bias Current**

While if you take the case of general-purpose op-amp like LM 741, in which the input bias current used to be in the range of nano-amperes.While if you see the high-precision op-amps, like AD 549, in that case, the input bias current used to be in the range of famto-amperes.

So, as you can see over here, the typical value of this input bias current is very small. And because of that for most of the applications, the effect of this input bias current will be negligible. But for the applications where you require very precise output, in that case, this bias current will become a critical parameter. So, now let’s see the effect of this input bias current on the feedback circuits.

**Effects Of Input Bias Current On Feedback Circuits**

So, here we have inverting op-amp circuit and for this configuration let’s see how the input bias current will produce a small amount of error in the output voltage. So, now to find the effect of this input bias current let’s assume that all the inputs which are applied to this op-amp circuit are zero.

So, we can consider this voltage Vin as zero volts. And the equivalent circuit will look like this. Now, here we are assuming that the input bias current IB- is flowing in the inverting terminal and the input bias current IB+ is flowing into the non-inverting terminal. So, now if you observe over here, this non-inverting terminal is at ground potential.

So, there will not be any effect of IB+ on the output voltage. And simply we can remove this IB+ source from the given circuit. And the equivalent circuit will now look like this. Now, here we are also assuming that the input offset voltage for the given op-amp is equal to zero volts. That means these two terminals are at the same potential. Now, if you observe over here this non-inverting terminal is at ground potential.

So, because of that, this node over here will also be at ground potential. And because of that, there will not be any flow of current through this resistor R1. And we can say that this current IB- is flowing through this resistor Rf. And because of that, the output voltage Vout will be equal to minus this current IB-, multiplied by this resistance Rf.

So, this is the error in the output voltage because of the input bias current. And this output voltage is commonly known as the output offset voltage because of this input bias current. And it is commonly denoted by the symbol Voo. So, as you can see over here, this output offset voltage is proportional to the input bias current and the feedback resistance.

So, as the value of this feedback resistance increases, the error in the output voltage will also increase. And this error can be minimized by connecting the offset compensation resistor at the non-inverting terminal.

**Input bias current compensation using the offset compensation resistor**

So, as shown in the figure, by connecting this offset compensation resistor, we can minimize the error in the output voltage. So, nowhere to find the total output offset voltage, we apply the superposition theorem. So, we will consider one current source at a time and we will find the error in the output voltage because of that input bias current. And later on, we will add the individual output voltages to get the total output offset voltage. So, first of all, let’s assume that this input bias current IB+ acting alone and this current IB- is equal to zero. And in that case, let’s find the output offset voltage.

So, now if you observe over here, the voltage at this node will be equal to this currentIB+ times this resistance Rc. Now, the output voltage Vout will be the DCgain of this circuit multiplied by the voltage at this terminal. And let’s say the output voltage over here is equal to output offset voltage 1.So, that is equal to this V+, multiplied by this (1+Rf/R1)Or we can say that, that is equal to IB+, multiplied by this resistance Rc times this(1+Rf/R1). So, this is the voltage that you will see in the output terminal because of this input bias current IB+.

Similarly, now let’s assume that this IB- current is acting alone and this current IB+ is equal to zero. And in that case, let’s say the output offset voltage is equal to Voo2. And we have already seen the value of this output offset voltage whenever this input bias current IB- is acting alone. So, we can say that the Voo2 will be equal to minus IB- times this feedback resistance Rf.

So, this is the output offset voltage whenever this input bias current IB- is acting alone. So, now let’s combine the individual output voltages to get the final output voltage. So, the total output voltage Vout is equal to this Voo1+ Voo2. That is equal to IB+ times this resistance Rc, multiplied by this (1+Rf/R1) plus (-IB-) times this feedback resistance Rf. So, this is the total output offset voltage because of this input bias currents.

So, now let’s find the value of this resistance Rc such that we can minimize the total output offset voltage. So, we can write this expression as IB+ times this resistance Rc, multiplied by this resistance (Rf)*(R1+Rf) divided by (R1*Rf(.So, basically, here we have multiplied and divided by this resistance Rf.And the second term will remain as it is.

So, if you observe over here this term is nothing but the inverse of the parallel combination of R1 and Rf. So, we can write this expression as IB+ times this resistance Rc *Rf, divided by the parallel combination of (R1 and Rf). And the second term will remain as it is.

Now, if here the value of Rc is the parallel combination of R1 and Rf, in that case, these two terms will get canceled out. And the total expression will get simplified to the (IB+ – IB-) times this resistance Rf. So, in this case, when Rc is equal to (R1||Rf), the expression will be get simplified to this difference between the two biasing currents, multiplied by the feedback resistance Rf. And if these two biasing currents are equaling that case the total output offset voltage will become zero volts. But if there is a mismatch between these two biasing currents in that case we can write this total output offset voltage as input offset current, multiplied by the resistance Rf.

Because we have seen that the input offset voltage is nothing but the difference between the two input biasing currents. So, this is the expression of the output offset voltage whenever the offset compensation resistor is connected at one terminal. Now, so far in our discussion, we have assumed that the input offset voltage for the given op-amp is zero volts. But if we also consider the effect of this input offset voltage then we can find the total output offset voltage, that will be present at the output terminal.

**Total Output Offset Voltage**

So, now if we assume that all the inputs which are applied to the circuit are zero, in that case, the effect of input bias currents and the input offset voltage can be represented by this circuit. So, for the given circuit the total output offset voltage will be equal to (1+Rf/R1) times the input offset voltage, plus Input offset current times the feedback resistance Rf.

So, basically here the first term represents the output offset voltage because of this input offset voltage. And the second term represents the output offset voltage because of this biasing currents.

So, this is the total output offset voltage whenever the input offset current and the input offset voltage are present at the input terminals. Now, as we have discussed in the last article, it is hard to predict the polarity of this input offset voltage and the input offset current. And because of that, these two terms can be either positive or negative.

But here we have assumed that these two terms are positive. And the maximum output offset voltage which will be present at the output terminal will be the summation of these individual output offset voltages. So, now let’s take one example, and through the example let’s see how these input offset voltage and the input bias current can affect the output voltage.

**Example Based On Input Bias Current and Input Offset Current**

So, here we have been given this non-inverting op-amp and for this op-amp, we have been given some parameters. So, basically, here we have been asked to find the total output offset voltage because of the input offset voltage (input bias current **and** input **offset** current) and the input bias currents. So, first of all, let’s find out the output voltage** V out** because of this input voltage. Now, as this circuit is connected in a non-inverting configuration, so the output voltage Voutwill be equal to (1+Rf/R1) times the input voltage Vin. Now, here the gain of this circuit is equal to 10.

So, the total output voltage Vout will be equal to 10 times the input voltage, which is equal to 10mV. So, the total output voltage Vout will be equal to 100 mV. So, this should be the output of the op-amp, if we consider all the input offset (**what is** input **offset voltage**) voltage and the input bias currents are zero. But because of these offset voltages and offset currents, there will be an error in the output voltage. So, now let’s find out the output offset voltage because of the input offset currents and the input offset voltage.

So, we have already seen the expression for the output offset voltage. That is equal to (1+ Rf/R1) times the input offset voltage, plus the input offsets current times the feedback resistance Rf. Now, we have derived this expression for the inverting op-amp configuration. But the same expression is valid for the non-inverting configuration a well. Because whenever we consider all the inputs are zero, at that time the inverting and the non-inverting configuration will be identical.

So, now let’s put the value of these parameters, and let’s find the total output offset voltage.So, if we put all the values then we can write this expression as10 times 0.5 mV, plus (50 nA) times this resistor Rf. And that is equal to 9 kilo-ohms. So, we can say that the total output offset voltage will be equal to 5mV + 450 uV. Or we can say that the total output offset voltage will be equal to 5.45 mV. So, this is the total output offset voltage because of the input bias current and the input offset voltage.

So, now the total voltage will be equal to this output voltage, plus-minus output offset voltage. That is equal to 100mV, plus-minus 5.45 mV. So, the total output voltage can be either 105mV or it can be roughly around 95 mV. So, because of these input bias currents (input bias current **of ic 741**) and the input offset voltage, there will be a 5 percent error in the output voltage.

moreover that the major contributing factor in this error is the input offset voltage. And in the last article, we have seen that the error which is introduced by this input offset voltage can be minimized by using the DC nulling circuits. While the error which is introduced by the input bias currents can be minimized by using the compensation resistor. So, that’s it for this article. I hope in this article you understood what is input offset current and what is input bias current. And how these bias currents affect the output of the op-amp and how we can reduce (**how to reduce** input bias current) the effect of these input bias currents.

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