As well as resistors and capacitors,
Operational Amplifiers, or
Op-amps as they are more commonly called, are one of the basic building blocks of Analogue Electronic Circuits.
Operational amplifiers
are linear devices that have all the properties required for nearly
ideal DC amplification and are therefore used extensively in signal
conditioning, filtering or to perform mathematical operations such as
add, subtract, integration and differentiation.
An
Operational Amplifier, or op-amp for short, is
fundamentally a voltage amplifying device designed to be used with
external feedback components such as resistors and capacitors between
its output and input terminals. These feedback components determine the
resulting function or “operation” of the amplifier and by virtue of the
different feedback configurations whether resistive, capacitive or both,
the amplifier can perform a variety of different operations, giving
rise to its name of “Operational Amplifier”.
An
Operational Amplifier is basically a three-terminal device which consists of two high impedance inputs, one called the
Inverting Input, marked with a negative or “minus” sign, (
- ) and the other one called the
Non-inverting Input, marked with a positive or “plus” sign (
+ ).
The third terminal represents the
Operational Amplifiers
output port which can both sink and source either a voltage or a
current. In a linear operational amplifier, the output signal is the
amplification factor, known as the amplifiers gain (
A )
multiplied by the value of the input signal and depending on the nature
of these input and output signals, there can be four different
classifications of operational amplifier gain.
- Voltage – Voltage “in” and Voltage “out”
- Current – Current “in” and Current “out”
- Transconductance – Voltage “in” and Current “out”
- Transresistance – Current “in” and Voltage “out”
Since most of the circuits dealing with operational amplifiers are
voltage amplifiers, we will limit the tutorials in this section to
voltage amplifiers only, (Vin and Vout).
The output voltage signal from an Operational Amplifier is the
difference between the signals being applied to its two individual
inputs. In other words, an op-amps output signal is the difference
between the two input signals as the input stage of an Operational
Amplifier is in fact a differential amplifier as shown below.
Differential Amplifier
The circuit below shows a generalized form of a differential amplifier with two inputs marked
V1 and
V2. The two identical transistors
TR1 and
TR2 are both biased at the same operating point with their emitters connected together and returned to the common rail,
-Vee by way of resistor
Re.
Differential Amplifier
The circuit operates from a dual supply
+Vcc and
-Vee which ensures a constant supply. The voltage that appears at the output,
Vout of the amplifier is the difference between the two input signals as the two base inputs are in
anti-phase with each other.
So as the forward bias of transistor,
TR1 is increased, the forward bias of transistor
TR2
is reduced and vice versa. Then if the two transistors are perfectly
matched, the current flowing through the common emitter resistor,
Re will remain constant.
Like the input signal, the output signal is also balanced and since
the collector voltages either swing in opposite directions (anti-phase)
or in the same direction (in-phase) the output voltage signal, taken
from between the two collectors is, assuming a perfectly balanced
circuit the zero difference between the two collector voltages.
This is known as the
Common Mode of Operation with the
common mode gain of the amplifier being the output gain when the input is zero.
Operational Amplifiers also have one output (although there are ones
with an additional differential output) of low impedance that is
referenced to a common ground terminal and it should ignore any common
mode signals that is, if an identical signal is applied to both the
inverting and non-inverting inputs there should no change to the output.
However, in real amplifiers there is always some variation and the
ratio of the change to the output voltage with regards to the change in
the common mode input voltage is called the
Common Mode Rejection Ratio or
CMRR.
Operational Amplifiers on their own have a very high open loop DC gain and by applying some form of
Negative Feedback
we can produce an operational amplifier circuit that has a very precise
gain characteristic that is dependant only on the feedback used. Note
that the term “open loop” means that there are no feedback components
used around the amplifier so the feedback path or loop is open.
An operational amplifier only responds to the difference between the
voltages on its two input terminals, known commonly as the “
Differential Input Voltage”
and not to their common potential. Then if the same voltage potential
is applied to both terminals the resultant output will be zero. An
Operational Amplifiers gain is commonly known as the
Open Loop Differential Gain, and is given the symbol (
Ao).
Equivalent Circuit of an Ideal Operational Amplifier
Op-amp Parameter and Idealised Characteristic
-
Open Loop Gain, (Avo)
-
Infinite – The main function of an operational amplifier is to
amplify the input signal and the more open loop gain it has the better.
Open-loop gain is the gain of the op-amp without positive or negative
feedback and for such an amplifier the gain will be infinite but typical
real values range from about 20,000 to 200,000.
-
Input impedance, (Zin)
-
Infinite – Input impedance is the ratio of input voltage to
input current and is assumed to be infinite to prevent any current
flowing from the source supply into the amplifiers input circuitry ( Iin = 0 ). Real op-amps have input leakage currents from a few pico-amps to a few milli-amps.
-
Output impedance, (Zout)
-
Zero – The output impedance of the ideal operational amplifier
is assumed to be zero acting as a perfect internal voltage source with
no internal resistance so that it can supply as much current as
necessary to the load. This internal resistance is effectively in series
with the load thereby reducing the output voltage available to the
load. Real op-amps have output impedances in the 100-20kΩ range.
-
Bandwidth, (BW)
-
Infinite – An ideal operational amplifier has an infinite
frequency response and can amplify any frequency signal from DC to the
highest AC frequencies so it is therefore assumed to have an infinite
bandwidth. With real op-amps, the bandwidth is limited by the
Gain-Bandwidth product (GB), which is equal to the frequency where the
amplifiers gain becomes unity.
-
Offset Voltage, (Vio)
-
Zero – The amplifiers output will be zero when the voltage
difference between the inverting and the non-inverting inputs is zero,
the same or when both inputs are grounded. Real op-amps have some amount
of output offset voltage.
From these “idealized” characteristics above, we can see that the input resistance is infinite, so
no current flows into either input terminal (the “current rule”) and that the
differential input offset voltage is zero (the “voltage rule”). It is important to remember these two properties as they will help us understand the workings of the
Operational Amplifier with regards to the analysis and design of op-amp circuits.
However, real
Operational Amplifiers such as the commonly available
uA741,
for example do not have infinite gain or bandwidth but have a typical
“Open Loop Gain” which is defined as the amplifiers output amplification
without any external feedback signals connected to it and for a typical
operational amplifier is about 100dB at DC (zero Hz). This output gain
decreases linearly with frequency down to “Unity Gain” or 1, at about
1MHz and this is shown in the following open loop gain response curve.
Open-loop Frequency Response Curve
From this frequency response curve we can see that the product of the
gain against frequency is constant at any point along the curve. Also
that the unity gain (0dB) frequency also determines the gain of the
amplifier at any point along the curve. This constant is generally known
as the
Gain Bandwidth Product or
GBP. Therefore:
GBP = Gain x Bandwidth or A x BW.
For example, from the graph above the gain of the amplifier at 100kHz
is given as 20dB or 10, then the gain bandwidth product is calculated
as:
GBP = A x BW = 10 x 100,000Hz = 1,000,000.
Similarly, the operational amplifiers gain at 1kHz = 60dB or 1000, therefore the GBP is given as:
GBP = A x BW = 1,000 x 1,000Hz = 1,000,000. The same!.
The
Voltage Gain (
AV) of the operational amplifier can be found using the following formula:
and in Decibels or (dB) is given as:
An Operational Amplifiers Bandwidth
The operational amplifiers bandwidth is the frequency range over which the voltage gain of the amplifier is above
70.7% or
-3dB (where 0dB is the maximum) of its maximum output value as shown below.
Here we have used the 40dB line as an example. The -3dB or 70.7% of
Vmax down point from the frequency response curve is given as
37dB.
Taking a line across until it intersects with the main GBP curve gives
us a frequency point just above the 10kHz line at about 12 to 15kHz. We
can now calculate this more accurately as we already know the GBP of the
amplifier, in this particular case 1MHz.
Operational Amplifier Example No1.
Using the formula
20 log (A), we can calculate the bandwidth of the amplifier as:
37 = 20 log A therefore, A = anti-log (37 ÷ 20) = 70.8
GBP ÷ A = Bandwidth, therefore, 1,000,000 ÷ 70.8 = 14,124Hz, or 14kHz
Then the bandwidth of the amplifier at a gain of 40dB is given as
14kHz as previously predicted from the graph.
Operational Amplifier Example No2.
If the gain of the operational amplifier was reduced by half to say
20dB
in the above frequency response curve, the -3dB point would now be at
17dB. This would then give the operational amplifier an overall gain of
7.08, therefore
A = 7.08.
If we use the same formula as above, this new gain would give us a bandwidth of approximately
141.2kHz,
ten times more than the frequency given at the 40dB point. It can
therefore be seen that by reducing the overall “open loop gain” of an
operational amplifier its bandwidth is increased and visa versa.
In other words, an operational amplifiers bandwidth is inversely proportional to its gain, (
A 1/∝ BW ).
Also, this -3dB corner frequency point is generally known as the “half
power point”, as the output power of the amplifier is at half its
maximum value as shown:
Operational Amplifiers Summary
We know now that an
Operational amplifiers is a very
high gain DC differential amplifier that uses one or more external
feedback networks to control its response and characteristics. We can
connect external resistors or capacitors to the op-amp in a number of
different ways to form basic “building Block” circuits such as,
Inverting, Non-Inverting, Voltage Follower, Summing, Differential,
Integrator and Differentiator type amplifiers.
Op-amp Symbol
An “ideal” or perfect
Operational Amplifier is a device with certain special characteristics such as infinite open-loop gain
Ao, infinite input resistance
Rin, zero output resistance
Rout, infinite bandwidth
0 to
∞ and zero offset (the output is exactly zero when the input is zero).
There are a very large number of operational amplifier IC’s available
to suit every possible application from standard bipolar, precision,
high-speed, low-noise, high-voltage, etc, in either standard
configuration or with internal Junction FET transistors.
Operational amplifiers are available in IC packages of either single,
dual or quad op-amps within one single device. The most commonly
available and used of all operational amplifiers in basic electronic
kits and projects is the industry standard
μA-741.
In the next tutorial about
Operational Amplifiers, we will use negative feedback connected around the op-amp to produce a standard closed-loop amplifier circuit called an
Inverting Amplifier circuit that produces an output signal which is 180
o “out-of-phase” with the input.