Common emitter amplifier design II
Posted 9th September 2010 at 07:27 PM by wakibaki
In the earlier post, basic common emitter amplifier design, I made reference to increasing the gain of the amplifier by bypassing the emitter resistor R[SIZE="1"]E[/SIZE].
In this case the gain referred to is the AC gain, which is the signal gain, and which is the gain we are primarily interested in with regard to audio amplifiers. The gain previously calculated was the DC gain, which was numerically identical to the AC gain, but since the amplifier was decoupled from the preceding stage with a capacitor, there was no DC applied to the transistor other than that provided by the bias network, which set the standing current to 1mA and the output voltage to 10V. DC gain and offset is important, because a decoupling cap can be avoided in some cases, but not here.
In the earlier post the gain was stated to be –R[SIZE="1"]C[/SIZE]/R[SIZE="1"]E[/SIZE]. This was a simplification, and, more strictly the gain is –R[SIZE="1"]C[/SIZE]/(R[SIZE="1"]E[/SIZE] + r[SIZE="1"]e[/SIZE]). r[SIZE="1"]e[/SIZE] is the value of the resistance between the base terminal of the transistor and the emitter terminal. It can be approximated to be 26mV/I[SIZE="1"]E[/SIZE](in mA), I[SIZE="1"]E[/SIZE] being the emitter current, which in the example given was 1mA. A voltage divided by a current (by Ohm’s law) is a resistance, in this case we get 26 Ohms. This gives a corrected value for the DC gain of the stage of ~9.75. It’s commonplace in engineering to treat such a value as indistinguishable from -10, since we would normally design the stage to have a gain exceeding that actually required by 10~20%. It’s easy to lose a bit of signal if it turns out to be necessary once the design is prototyped
If we could nullify the effect of the emitter resistor R[SIZE="1"]E[/SIZE], the AC gain of the stage would become (-)R[SIZE="1"]C[/SIZE]/r[SIZE="1"]e[/SIZE] or (-)10,000/26 = (-)384.6, a considerable increase (~40*) over the previously calculated figure.
If we put a capacitor of suitable value in parallel with R[SIZE="1"]E[/SIZE] then it acts as a short to ground for AC purposes. As far as the AC gain calculation is concerned, R[SIZE="1"]E[/SIZE] will disappear.
Since we have already chosen for this stage to have an input low frequency -3dB point of 30Hz, it makes sense to design the bypass for 30Hz.
This capacitor is chosen by making its reactance small compared with r[SIZE="1"]e[/SIZE]. The actual resistance to ground which the capacitor parallels is a combination of R[SIZE="1"]E[/SIZE] in parallel with (r[SIZE="1"]e[/SIZE] in series with [the resistances on the other side of the transistor [I]divided[/I] in this case by h[SIZE="1"]fe[/SIZE]]). r[SIZE="1"]e[/SIZE] is a reasonable first approximation.
X[SIZE="1"]c[/SIZE] = 1/(2*pi*f*C)
26 = 1/(2*pi*30*C)
C=200uF
[ATTACH]255[/ATTACH]
The actual low frequency cutoff should, where critical, be determined by measurement, or at least by simulation. Not all simulators can be depended upon to simulate this accurately.
Some words of caution.
As is usually the case, the design involves a number of trade-offs, a reduction of input impedance accompanies the increase in gain.
The input impedance is reduced drastically to 2.5k (h[SIZE="1"]fe[/SIZE]*r[SIZE="1"]e[/SIZE]).
When designing a CE amplifier the voltage drop across the emitter resistor should not be made small in comparison to the base-emitter voltage drop (0.6V). This can result in reduced bias stability with regard to temperature, because the base emitter voltage drop is temperature-dependent.
Bypassing the entire emitter resistor makes the gain dependent on h[SIZE="1"]fe[/SIZE] rather than R[SIZE="1"]C[/SIZE] and R[SIZE="1"]E[/SIZE]
These three problems can be addressed by either splitting the emitter resistor into an unbypassed part above a bypassed part, or putting a resistor in series with the capacitor. In this case the gain will be determined by either the unbypassed upper resistor or the resistance in series with the capacitance (in combination with re), although the gain available will inevitably be less that the maximum available, which is sometimes a consideration, although less so in audio.
[ATTACH]256[/ATTACH]
[ATTACH]257[/ATTACH]
This brief appreciation of the design process is intended to give readers a start in understanding and analyzing published circuits which are frequently more complex than the basic common emitter amplifier presented here. Unless the reader is seriously interested in amplifier design, as opposed to general electronics, this level of understanding frequently proves adequate for most people's purposes.
w
In this case the gain referred to is the AC gain, which is the signal gain, and which is the gain we are primarily interested in with regard to audio amplifiers. The gain previously calculated was the DC gain, which was numerically identical to the AC gain, but since the amplifier was decoupled from the preceding stage with a capacitor, there was no DC applied to the transistor other than that provided by the bias network, which set the standing current to 1mA and the output voltage to 10V. DC gain and offset is important, because a decoupling cap can be avoided in some cases, but not here.
In the earlier post the gain was stated to be –R[SIZE="1"]C[/SIZE]/R[SIZE="1"]E[/SIZE]. This was a simplification, and, more strictly the gain is –R[SIZE="1"]C[/SIZE]/(R[SIZE="1"]E[/SIZE] + r[SIZE="1"]e[/SIZE]). r[SIZE="1"]e[/SIZE] is the value of the resistance between the base terminal of the transistor and the emitter terminal. It can be approximated to be 26mV/I[SIZE="1"]E[/SIZE](in mA), I[SIZE="1"]E[/SIZE] being the emitter current, which in the example given was 1mA. A voltage divided by a current (by Ohm’s law) is a resistance, in this case we get 26 Ohms. This gives a corrected value for the DC gain of the stage of ~9.75. It’s commonplace in engineering to treat such a value as indistinguishable from -10, since we would normally design the stage to have a gain exceeding that actually required by 10~20%. It’s easy to lose a bit of signal if it turns out to be necessary once the design is prototyped
If we could nullify the effect of the emitter resistor R[SIZE="1"]E[/SIZE], the AC gain of the stage would become (-)R[SIZE="1"]C[/SIZE]/r[SIZE="1"]e[/SIZE] or (-)10,000/26 = (-)384.6, a considerable increase (~40*) over the previously calculated figure.
If we put a capacitor of suitable value in parallel with R[SIZE="1"]E[/SIZE] then it acts as a short to ground for AC purposes. As far as the AC gain calculation is concerned, R[SIZE="1"]E[/SIZE] will disappear.
Since we have already chosen for this stage to have an input low frequency -3dB point of 30Hz, it makes sense to design the bypass for 30Hz.
This capacitor is chosen by making its reactance small compared with r[SIZE="1"]e[/SIZE]. The actual resistance to ground which the capacitor parallels is a combination of R[SIZE="1"]E[/SIZE] in parallel with (r[SIZE="1"]e[/SIZE] in series with [the resistances on the other side of the transistor [I]divided[/I] in this case by h[SIZE="1"]fe[/SIZE]]). r[SIZE="1"]e[/SIZE] is a reasonable first approximation.
X[SIZE="1"]c[/SIZE] = 1/(2*pi*f*C)
26 = 1/(2*pi*30*C)
C=200uF
[ATTACH]255[/ATTACH]
The actual low frequency cutoff should, where critical, be determined by measurement, or at least by simulation. Not all simulators can be depended upon to simulate this accurately.
Some words of caution.
As is usually the case, the design involves a number of trade-offs, a reduction of input impedance accompanies the increase in gain.
The input impedance is reduced drastically to 2.5k (h[SIZE="1"]fe[/SIZE]*r[SIZE="1"]e[/SIZE]).
When designing a CE amplifier the voltage drop across the emitter resistor should not be made small in comparison to the base-emitter voltage drop (0.6V). This can result in reduced bias stability with regard to temperature, because the base emitter voltage drop is temperature-dependent.
Bypassing the entire emitter resistor makes the gain dependent on h[SIZE="1"]fe[/SIZE] rather than R[SIZE="1"]C[/SIZE] and R[SIZE="1"]E[/SIZE]
These three problems can be addressed by either splitting the emitter resistor into an unbypassed part above a bypassed part, or putting a resistor in series with the capacitor. In this case the gain will be determined by either the unbypassed upper resistor or the resistance in series with the capacitance (in combination with re), although the gain available will inevitably be less that the maximum available, which is sometimes a consideration, although less so in audio.
[ATTACH]256[/ATTACH]
[ATTACH]257[/ATTACH]
This brief appreciation of the design process is intended to give readers a start in understanding and analyzing published circuits which are frequently more complex than the basic common emitter amplifier presented here. Unless the reader is seriously interested in amplifier design, as opposed to general electronics, this level of understanding frequently proves adequate for most people's purposes.
w
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