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Electronics I Laboratory Manual

# Op-Amp Characteristics

When buying operational amplifiers1 the manufacturer will specify certain electrical and operational conditions that the user must know in order to use the device wisely.  The data sheet provided by the manufacturer when a component is bought is a wealth of information about the expected performance of the device.  Normally the information provided is very difficult, if not impossible, to obtain on one’s own.  To the manufacturer the data specification sheet tells the user what to expect from the device or component.

In this experiment you will have the opportunity to determine some characteristics of Operational Amplifiers, and you will compare your values with the specifications provided by the manufacturer.  The Op-Amp parameters discussed in this experiment are: Input Offset and how to correct it, Open-loop Voltage Gain, Maximum Output Voltage, Bandwidth, Common-Mode Rejection Ratio, and Slew Rate.  A brief explanation of each one follows.

1 Like any other device.

Input Offset Voltage

Figure 22.1: If there is a mismatch of the
VBE’s (i.e., VB1>VB2),
a small output voltage
is produced at the output.

When the ideal operational amplifier has no differential input voltage applied to it,the ideal op-amp produces zero volts in the output.  In real amplifiers, however, a small DC voltage is generated at the output when no differential input is applied.  The cause of this is the mismatch that always exists of the base-to-emitter voltages (VB1 and VB2) as shown in Figure 22.1.  As you can see, the output (differential) voltage is the difference between the two collector voltages generated, or in equation form

 (22.1)

A mismatch in the base voltages of the transistors results in a mismatch in the base currents and, in turn, produces a mismatch in the collector currents.  This error produces a non-zero value of the output voltage (Vo), assuming that the collector resistances are identical.

In order to compensate for this output error voltage, the manufacturer specifies that at the input we should apply a voltage to force the differential output to zero volts.  This voltage is called the input offset voltage, Vos and it is equal to the differential DC voltage given by

 (22.2)

The input offset voltage is the difference in the voltage between the inputs that is necessary to force the output differential voltage to zero.  Figure 22.2 demonstrates these ideas.

To compensate an op-amp for the mismatch in output voltage the manufacturer of chips provides two pins in the chip where you must apply this voltage (normally through a resistor).  For the case of the LM741 IC chip these pins are 1 and 5.  The method of compensation is shown in Figure 22.6.

Open-Loop Voltage Gain

The open-loop voltage gain expressed as Aol or Ad is the voltage gain of the amplifier when there is no external feedback connected to it.  This gain, for the case of the differential amplifier, was presented in the previous experiment2.  This gain is very large for a good op-amp.  The larger the open-loop gain the more versatile is the amplifier.  Op-amps may have open-loop gains as high as 1,000,000.  A typical value is around 200,000 or less.  The LM741 has a minimum gain specified 20,000 and a typical value of 200,000.  No maximum value is specified by the manufacturer.

With open-loop gain values so big even a very small signal at the input may cause the op-amp to sit at its positive or negative saturation value (maximum value3).

Figure 22.2:  The input offset voltage (Vos) is the
voltage needed to force the output voltage to zero
(Voand 0V).  Vos is applied at one of the two inputs.

For example, an input signal as small as 70µV applied at the input of a LM741 chip (assuming Aol = 200,000) will saturate the amplifier (typical saturation value is ±14V).  Because of this fact when measuring the open-loop gain one should use a voltage divider at the input and calculate4 the input voltage, since it will be too small to accurately measure.

Open-loop gains are better measured by applying a dc voltage (f = 0 Hz) since the open-loop bandwidth is very small (for the LM741 the bandwidth extends only to 10 Hz).

2 See Section 21.3.2

3 See Section 22.3.3

4 It is very difficult to measure.

Maximum Output Voltage

As we have seen in the last section the open-loop voltage gain of an op-amp is very large.  For an amplifier to operate in its linear region5 the input signal has to very small (in general in the order of µV).  If a larger signal is applied the output voltage reaches a maximum (or minimum) value.  Any increase in the input signal amplitude will not cause an increase in the output.  This condition is called saturation.  Like a typical transistor, the op-amp will saturate when the input signal is beyond certain limits.  We define the maximum output voltage swing (saturation) as the range of values that the op-amp output can reach.  The saturation values are directly related to both the values chosen for the split power supply (Vcc and Vee6), and to the internal circuitry of the amplifier.  For the case of the LM741 the maximum peak-to-peak output voltage swing specifications are a minimum of ±12V, and a typical value of ±14V when the power supply values are ±15V and the load is ≥ 10kΩ.

5 In other words, to operate as an linear amplifier.

6 Sometimes called + Vcc and -Vcc

Common-Mode Rejection Ratio

The common-mode-rejection ratio (CMRR) was discussed in Experiment No. 21 in relation to the differential amplifier7.  As you should remember, the CMRR is a measurement of how well the op-amp can reject two identical signals applied at the inputs.  The CMRR describes how well the amplifier amplifies differential (desired) signals while attenuating common-mode (undesired) signals8.  The ideal amplifier has a CMRR equal to infinity.  This means the output of the amplifier will be zero when the same signal is applied to both input terminals (common-mode).  In real op-amps, however, when common-mode signals are applied, the output will generate a small9 voltage.  An amplifier with a high CMRR is able to virtually eliminate these undesired signals from the output.

The CMRR is defined as the ratio of the open-loop gain (Aol) to the common-mode gain (Ac), or

 (22.3)

Because this value is large, normally it is expressed in decibels as follows:

 (22.4)

Figure 22.3:  (a) Circuit to measure the slew rate. (b)
Step input voltage and the resulting output voltage.

7 See Section 21.3.3.

8 Like noise, and the interference voltages such as the 60 Hz power-supply ripple due to pick-up of radiated energy.

9 But very undesirable.

Slew Rate

The slew rate is defined as the maximum rate of change of the output voltage in response to a step input voltage.  The slew rate is a measure of how fast the op-amp can respond to changes in the input.  This is illustrated in Figure 22.3.  In part (a) of the figure we present a typical circuit used to measure the slew rate10.  This circuit gives the worst-case scenario.  A pulse is applied to the input and the output voltage is measured as is indicated in Figure 22.3(b).  As you can see the output slew from its lower value to its upper limit.  A certain time interval is needed for the output voltage to go from –Vmax to +Vmax once the input step is applied.  If the operational amplifier were ideal it would have an infinity slew rate.  In this particular case the output voltage would look exactly the same as the input voltage at very high frequencies.  As you can see, for a real op-amp it takes a finite amount of time for the signal to switch from one voltage extreme to the other.  We define the slew rate as follows:

 (22.5)

and  is the time interval (in the figure this is called T).  The unit of slew rate is volts divided by time.  A typical unit is volts per microseconds, (V/µs).  The slew rate is dependent upon the frequency response of the internal stages of the op-amp.  Thus, the higher the slew rate, the better the frequency response of the amplifier.

10 This circuit is called a unity-gain amplifier.  We will study this circuit in Experiment No. 23.

Bandwidth

Figure 22.4: Frequency response of an op-amp.

The bandwidth of an op-amp is the range of frequencies that will produce an output voltage without a big attenuation.  A typical frequency response of an op-amp is shown in Figure 22.4.  In the figure we can distinguish three important bandwidths, namely

Open-loop bandwidth.  This is a very small bandwidth.  It is measured with no feedback connected to the op-amp.

Close-loop bandwidth.  It is the bandwidth of the op-amp when there is a feedback connection.  When in feedback the gain of the amplifier can be made to have basically any value lower than the open-loop gain.  As the gain is lowered the bandwidth increases, as you can see.

Open-loop bandwidth.  This is the bandwidth measured when the gain of the amplifier is equal to 1.  Many times this is the specified bandwidth given by manufacturers.

Gain-Bandwidth Product

The bandwidth and the gain of an amplifier are inversely proportional.  If you decrease the gain (connecting the amplifier in feedback, for instance) the bandwidth will increase and vice versa.  This relationship happens in such a way that the product of the bandwidth and the gain is always a constant11.  Based on this idea and looking at Figure 22.4 we can write the following equations

 = unity-gain bandwidth (22.6)

where Aol and Acl are the open-loop and closed-loop gains respectively; fc(ol), fc(cl) and f1 are the open-loop, closed-loop and unity-gain critical frequencies (same as bandwidth in this case) respectively.

11 For this to be true the roll-off rate of the frequency response should remain constant.

The LM741 Chip

Figure 22.5: Pin-out of the LM741 IC Chip.

The LM741 is an 8-pin chip of one operational amplifier.  The pin-out of the chip is shown in Figure 22.5.  As you can see the –input and +input are pins 2 and 5 respectively, whereas the output is taken from pin 6.  The supplies are applied at pin 7 for the positive voltage (+Vcc) and pin 4 for the negative supply (-Vcc or VEE).  Pins 1 and 5 are used to compensate the op-amp for the offset voltage.  Pin 8 is not connected (NC).

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