Black Box Approach to Amplifiers
To use A Back Box approach to an electronic device is to understand its basic characteristics without any
concern for what happens “inside” the device. It allows the user to concentrate on understanding these
characteristics without being distracted by how the device actually works.
A Black Box Amplifier
A block diagram of a voltage amplifier is shown.
Basic Characteristics
The characteristics of interest for an amplifier are:
•
Voltage Gain – AV
•
Input Resistance – RIN
•
Output Resistance – ROUT
•
Bandwidth – BW
Voltage Gain – AV
The basic purpose of an amplifier is to accept a small voltage signal at the input and make it larger at the
output.
The definition of Voltage Gain is
AV = VOUT/VIN
Voltage Gain has no units
An Ideal Amplifier has an infinite voltage gain but for practical amplifiers the voltage ranges from small,
to moderate to large values. A good quality practical amplifier has a large voltage gain.
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Measuring Voltage Gain
To measure the voltage gain of an amplifier involves connecting an AC input signal (a sine wave is used
because it is an AC signal with well known properties) of a known amplitude at the input and then
measures the amplitude of the output signal. The voltage gain is determined by dividing the magnitude
of VOUT by VIN.
Amplifiers can also be classified as Non-Inverting (the input and output waveforms are in phase) or
Inverting (the input and output waveforms are 180° out of phase).
Non-Inverting Amplifier Waveforms
Inverting Amplifier Waveforms
Question
What is the voltage gain for the amplifier represented by the Inverting Amplifier waveforms?
From the graph: VIN = 4 V P-P, VOUT = 10 V P-P
so
AV = VOUT/VIN = 10 V P-P/4 V P-P = 2.5
Input Resistance
The Input Resistance of an amplifier should be large. For an Ideal Amplifier the value of Input Resistance
is infinite. An infinite Input resistance means that the amplifier would not draw any current from the
voltage source circuit to which it is connected and as a result would not load down the source voltage
VS.
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The value of Vin is derived by using voltage divider on the circuit consisting of VS, RS, and RIN.
VIN = RIN/(RS + RIN) x VS
For VIN to be close in value to VS the value of RIN must be much larger than the value of RS.
For VIN ≈ VS RIN >> RS
For practical amplifiers the Input Resistance ranges from small, to moderate to large values. A good
quality practical amplifier has a large input resistance.
Measuring Input Resistance
The circuit configuration shown can be used to measure RIN. The resistor RS is made a variable resistor
or potentiometer.
Procedure:
•
Set VS to a convenient value and RS to zero Ω.
•
Measure the value of VIN.
•
Adjust the RS until VIN decreases to ½ of the value just measured.
•
Remove RS from the circuit and measure its value with a DVM set to Ω.
•
This value of RS is equal to RIN of the circuit (voltage divider principle).
Output Resistance
The output resistance of the amplifier is modeled in series with a current source (IC = β x IB) as shown in
the drawing. An ideal amplifier has a zero output resistance. A good quality practical amplifier has a
very small output resistance.
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Measuring Output Resistance
This is done in a similar manner to the procedure for measuring RIN. The output voltage is measured
with no load resistor attached. A variable load resistor is connected to VOUT and it is adjusted until VOUT
is one half of the “no-load” voltage. The variable resistor is removed from the circuit and its value is
measured. This measured value is the value of ROUT.
Bandwidth of Amplifier
The bandwidth (BW) of an amplifier specifies the range of frequencies that the voltage gain is more or
less a constant value. An ideal amplifier has an infinite bandwidth.
Real or practical amplifiers should have large finite bandwidths. The bandwidth as shown in the graph is
specified from DC to a frequency called the Corner Frequency.
AV
Corner frequency
Bandwidth
Freq
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The corner frequency is the frequency where the Voltage Gain AV has dropped to 0.707 of its original
value.
AC Amplifier
Some amplifiers because of their design have Upper and Lower corner frequencies as shown below. The
Bandwidth is measured between these points.
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