■ FIGURE 8. Gain and frequency
response of single and cascade
bandwidth to work with.
Figure 8 shows the
simulation results for both
the single and cascade
connections of the two
For a single amplifier, the
low frequency gain is the
square root of 1,000 ( 30
dB) while the simulated
bandwidth is 31. 9 kHz —
almost exactly what we
predicted. For the cascade, the low frequency gain is
1,000 ( 60 dB) while the overall bandwidth is reduced to
20. 7 kHz. This again is in excellent agreement with the
value predicted by bandwidth shrinkage theory.
f0 = 20. 7 kHz
Rf +1 =
f0 = 31. 9 kHz
1.0Hz 10Hz 100Hz
Freque n cy
Op-amps are usually not powerful enough to take a
small signal input from a microphone or head unit and
amplify the source sufficiently to directly drive a speaker.
For example, assume the signal is generated at a frequency
of 1 kHz and the speaker requires a ±1 V peak swing at
the output for adequate volume. A one volt peak swing
across an eight ohm speaker (typical for a small speaker)
requires that the op-amp deliver a peak current of 125 mA
(1V divided by eight ohms) — which is far in excess of the
uA741’s maximum rating of 25 mA.
The solution to this problem is to provide additional
current amplification using the complimentary Class
AB emitter follower shown in Figure 9. In this circuit,
resistors R3 and R4 along with diodes D1 and D2
provide base-emitter bias sufficient to set transistors
Q1 and Q2 just at the edge of conduction. This is
necessary in order to minimize crossover distortion
as the transistors alternately switch on and off.
Additionally, connecting the feedback resistor R2
across the load (R5) forces the amplifier output
voltage to closely track the input signal waveform,
which almost totally eliminates output stage distortion.
One can observe that the resistors R1 and R2
in the circuit set the midband gain to about 24 V/V;
this should allow us to reach our necessary output swing
— provided we are at a midband frequency. We can check
to see if 1 kHz falls in the midband range by recalling that
the uA741 has a GBW of 1 MHz. Thus, a midband gain
requirement of 100 should result in a 40 kHz bandwidth.
This provides sufficient bandwidth to avoid the gain roll-off
that occurs as we approach the amplifier cutoff frequency.
Figure 10 displays 10 milliseconds of the output
waveform that results from performing a transient analysis
of the circuit when driven by a 1 kHz voltage source. The
output waveform appears to be almost perfectly sinusoidal
without evidence of crossover distortion at the zero
crossings of the waveform. It is easy to verify this by using
the Fast Fourier Transform (FFT) function of PSpice to
compute the frequency spectrum of the output waveform.
In this case, the transient simulation was run for one
second to create 1,000 cycles of the 1 kHz output waveform
to obtain sufficient resolution in the frequency spectrum
■ FIGURE 9.
DC = 5V
C1 100 μF
+ - OS1
Figure 9 Parts List
RESISTORS (1/4 watt) SEMICONDUCTORS
■ R1 1KΩ ■ U1 uA741 op-amp
■ R2 24KΩ ■ D1, D2 1N4148 diode
■ R3, R4 510 Ω ■ Q1 2N3904
■ R5 8 Ω ■ Q2 2N3906
■ C1,C2 100 μF, 25V ■ 5V dual power supply
electrolytic or batteries ■
8 Ω speaker
FREQUENCY = 1 kHz
AMPLITUDE = 42 mV
DC = 5V
C2 100 μF
October 2008 53