Ideal Operational
Amplifiers
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 ideal 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 op-amps 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 amplified output
signal of an Operational Amplifier is the difference between the two
signals being applied to the two inputs. In other words the output
signal is a differential signal between the two inputs and 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
V1and 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.
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
theCommon Mode of Operation with the common mode gain of the
amplifier being the output gain when the input is zero.
Ideal 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. 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 theOpen Loop Differential Gain,
and is given the symbol (Ao).
Equivalent Circuit for
Ideal Operational Amplifiers
Op-amp Idealized
Characteristics
PARAMETER AND IT'S IDEALIZED 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 an
ideal 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-impedance in the 100-20Ω 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 = 20dB or 10, then
the
GBP = 100,000Hz x 10 =
1,000,000.
Similarly, a gain at 1kHz
= 60dB or 1000, therefore the
GBP = 1,000 x 1,000 =
1,000,000. The same!.
The Voltage Gain (A) of
the amplifier can be found using the following formula:
Voltage
Gain(A)=V(out)/V(in)
and in Decibels or (dB)
is given as:
20log(A)
20log(V(out)/V(in))
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.
Example No1.
Using the formula 20log
(A), we can calculate the bandwidth of the amplifier as:
37 = 20logA 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.
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
approximately141.2kHz, ten times more than 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
proportional to its gain. Also, this -3dB point is generally known as
the "half power point", as the output power of the
amplifier is at half its maximum value at this value.
Operational Amplifiers
Summary
OP -AMP SYMBOL
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
JFET 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 180o"out-of-phase" with the input.