Download Power Amplifier Circuits

Section F3: Power Amplifier Circuits - Class A Operation
As mentioned in the previous section, our studies of BJT and FET amplifiers
to date have been of the Class A designation since the output signal is an
amplified version of the entire input. What we’re going to look at now are
some of the useful circuit configurations for Class A power amplifiers, where
the category is determined by the coupling mechanism. Please note that the
configurations we will be discussing are by no means the only configurations
available. Whatever strategy we take; remember that we want to maximize
power delivered to the output. This involves a large current gain and
impedance matching to the load at the output stage.
There is some difficulty in this chapter with the orientation of the
polarized capacitors. I have attempted to make appropriate changes,
both in the notes and the assigned homework, but please be aware
of this problem in case I miss something (but let me know if I do,
ok?)
Inductively Coupled Amplifier
An example of an inductively coupled
amplifier is presented to the right and
is based on Figure 8.6a of your text.
This schematic is our old friend the
common emitter BJT amplifier with an
inductor replacing the collector resistor
RC. Recall that the effective load for a
CE amplifier was RC||RL, and that the
effective load was less than either RC or
RL. Using a properly sized inductor
instead of a resistor in the collector leg
will allow us to increase the output
voltage and, as we’ll see a little later,
increase the efficiency of the amplifier
circuit.
By analyzing the expression for the impedance of an inductor
Z L = Rcoil + jωL = Rcoil + j2πfL ,
we can see that the impedance consists of the internal resistance of the coil,
Rcoil, and an inductive reactance term that is dependent upon the frequency
of operation, ωL. At dc (ω=0), ZL=Rcoil, while at high frequencies the ωL term
dominates and becomes very large. Harking back to circuit days, remember
that we modeled an ideal inductor as a short circuit to dc and an open circuit
to large frequencies. To make effective use of this configuration, we want to
approximate the behavior of the ideal inductor as closely as possible.
Therefore, for dc we will require
Rcoil << Rload
and
Rcoil << RE ,
(Equation 8.2)
and for the lowest input signal frequency ωL=2πfL (which will yield the
minimum reactive impedance)
ω L L >> Rload .
(Equation 8.1)
If the above conditions are met, we may approximate the ac and dc
equivalent resistances as
Rdc = Rcoil + RE ≅ RE
and
Rac = Z L || Rload ≅ Rload .
Figure 8.6b, reproduced to
the right, illustrates the
load lines for the inductively
coupled amplifier. Note that
it is assumed in this figure
(from the slopes of the load
lines) that RE<< Rload. To
observe the effect on the
load lines of replacing RC
with
L,
please
review
Section
C8
and,
in
particular, Figure 4.17.
Choosing the Q-point for maximum swing (as we have done so many times
before) and using the approximations for ac and dc resistances above, we
get
I CQ =
VCC
VCC
=
.
Rac + Rdc
Rload + RE
(Equations 8.3 & 8.4)
By using the assumption implied in the load lines above, RE << Rload, the
voltage drop across both Rcoil and RE may be considered negligible and we
may make the approximation VCEQ ≈ VCC. If all this works out, the expression
for ICQ may be further simplified as
I CQ ≅
VCC
V
≈ CE .
Rload
Rload
(Equation 8.5, Modified)
Now, realizing that the Q-point is in the center of the load line, we may
project V’CC to be equal to 2VCC. This is actually pretty cool – the inductor
stores energy in its magnetic field during the conducting cycle and
essentially acts like a second VCC source in series with the dc power supply.
So…by using an inductor in the amplifier circuitry, we have created an
available voltage swing that is equivalent to doubling the supply voltage.
The remainder of the design for this amplifier configuration follows the
standard process developed for the common emitter amplifier in Section D2
with the appropriate modifications arising from the assumptions as to the
inductive impedance; i.e., |ZL|≈0 for dc and |ZL|>>Rload for all input
frequencies. Specifically,
Rin = RB || rπ
AV =
− Rload
re
Rout = Rcoil
Ai =
− RB
RB
β
.
+ re
To define the conversion efficiency (η), we develop the ratio of ac power
delivered to the load to the dc power supplied by the source (please review
Section C7 for our discussion of Power Considerations from last semester).
Keeping our assumption that RE << Rload, so that VCEQ ≈ VCC and ICQ ≈
VCC/Rload, we may derive the power supplied by the voltage source as follows
(your author skipped a few steps)
Pin (dc) =
2
VCC
2
(Rcoil + RE )
+ VCEQ I CQ + I CQ
R1 + R2
2
⎛V
VCC
=
+ (VCC )⎜⎜ CC
R1 + R2
⎝ Rload
⎛
1
1
2
⎜
= VCC
⎜R + R + R
load
2
⎝ 1
2
⎞
⎟⎟ (Rcoil + RE ) .
⎠
R + RE ⎞
⎟
+ coil 2
Rload ⎟⎠
⎞ ⎛ VCC
⎟⎟ + ⎜⎜
⎠ ⎝ Rload
So…recalling that R1 and R2 are pretty huge when compared to the other
resistances and we’ve defined Rcoil and RE to be much less than Rload, the
second term in the parentheses is much larger than the other two.
Therefore,
Pin (dc) =
2
VCC
Rload
,
(Equation 8.6)
while the ac power delivered to the load, assuming the current is sinusoidal
with a maximum amplitude Iloadmax (and the Q-point is in the center of the ac
load line so Iloadmax=ICQ), is
Pout (ac) = Pload =
2
VCC
1 2
1 2
.
I load max Rload = I CQ
Rload =
2
2
2Rload
(Equation 8.7)
Note that the expressions above are in keeping with the CE derivations of
Section C7. Specifically, if RE is negligible, then VCEQ ≈ VCC and the average
power dissipated will range between Pout(ac) and Pin(dc) as defined in
Equations 8.6 and 8.7. It is worth noting that the true conversion efficiency
must take into account the power dissipated in the bias circuitry which would
effectively increase Pin(dc). Through our assumptions, we have neglected
these losses and the conversion efficiency below is an absolute maximum.
Using Equation 4.37, we may define the conversion efficiency (in percent) as
2
Pout (ac)
VCC
/(2Rload )
η(%) =
* 100 =
* 100 = 50% .
2
Pin (dc )
VCC / Rload
(Equation 8.8)
Your author states that if the inductor is replaced with a resistor, that the
maximum efficiency of the amplifier will be 25%. This is actually somewhat
optimistic. He has assumed that the load resistance and collector resistance
are equal so that the current is divided equally. This is okay - it will halve
the maximum power to the load and therefore halve the amplifier conversion
efficiency, all else constant. The problem with this approach is that he does
not consider the effect on the dc input power (even if we can still neglect RE,
we must include the losses in RC) and the effect on the load lines (VCEQ will
no longer be VCC, etc.). So… take it for what it’s worth… but 25% is probably
pretty large!
Transformer Coupled Power Amplifier
The other Class A power amplifier
configuration we’re going to be
considering is the transformer coupled
circuit shown to the right (a modified
version of Figure 8.7 in your text). This
figure illustrates an EF (CC) amplifier
that uses a transformer to couple the load for ac operation.
Note that the ac and dc resistances are seen at the primary side of the
transformer (please see Section D7 for a review on transformer coupled
amplifiers). For Rdc, all we have is the resistance of the primary coil. This is
usually quite small and will be considered negligible for our purposes,
yielding
Rdc = R primary ≅ 0 .
For ac operation, the resistance seen at the emitter is the reflected load
impedance. Recall that the relationship between a resistance seen at the
primary to a resistance at the secondary is determined by the turns ratio:
⎛N
R1 = R2 ⎜⎜ 1
⎝ N2
⎞
⎟⎟
⎠
2
,
and a in the above figure is equal to N1/N2. We may therefore express Rac as
Rac = a 2 RL .
(Equation 8.9)
The
load
lines
for
the
transformer-coupled amplifier are
illustrated in the figure to the
right (a modified version of Figure
8.7b). This representation is
extremely similar to that for the
inductively coupled amplifier and,
except for the value of the ac
resistance, will proceed in exactly
the same manner.
Designing for maximum output
swing, we place the Q-point in the center of the load line by
I CQ =
VCC
V
≅ 2CC .
Rac + Rdc
a RL
(Equation 8.10)
The remainder of the amplifier design follows the process developed for
emitter follower (common collector) amplifiers in Section D4.
Following the procedure discussed for the inductively coupled amplifier
above, the maximum power conversion efficiency of the transformer coupled
power amplifier is also 50%. Note that even though the EF configuration has
a voltage gain near unity, the turns ratio of the transformer determines the
voltage gain to the load through
⎛N
v 2 = v 1 ⎜⎜ 2
⎝ N1
⎞ v1
⎟⎟ =
a
⎠
.
Finally, note that the transformer-coupled amplifier offers a significant
advantage in that the transformer can match the load impedance to the
amplifier output impedance for maximum power transfer by choosing the
proper turns ratio.