The Common Emitter (CE) amplifier’s emitter resistor is one of several key components used to set the gain of the amplifier stage. It performs this operation by limiting the amount of negative feedback applied to the amplifier stage. The short answer is that the emitter bypass capacitor increases the amplifier’s gain by suppressing the feedback.
This engineering brief presents a representative Common Emitter (CE) and then explores the operation of the emitter bypass capacitor. We will explore the capacitor’s impact on gain, distortion, and frequency response. We will also explore the benefits of a partially bypassed emitter resistor. This is accomplished by adjusting R4 (shown in Figure 1) to change the proportion of the emitter resistor (self) that is bypassed.
You can load an interactive simulation of this circuit on MultisimLive .
Figure 1: Representative Class A CE amplifier featuring the 2N3904 transistor. Variable resistor R4 sets the ratio of the emitter resistor to be bypassed.
Gain demonstration
Let’s begin our exploration by observing the impact of the emitter bypass capacitor on the amplifier’s gain. Figure 2 shows the amplifier’s response when variable resistor R4 is adjusted in 10% increments. Observe that the response is nonlinear with gain increasing as C2 is connected directly to the transistor’s emitter. The diagram also suggests that higher gain is associated with increased distortion.
Note that Figure 2 was automatically generated using the “parameter” function of Multisim live. This tool allows the user to focus on a component and then vary the value. In this example, the tool is used to adjust R4 from 0, 14, 28, 42 Ω and so on until the full 140 Ω is reached. For each setting, it plots the corresponding amplifier output.
Figure 2: Response of the amplifier as variable resistor R4 is adjusted: green input, blue output). Each curve represents the output for a given potentiometer setting with a curve for each 10% increment. The highest gain with greatest distortion occurs when the C2 is connected directly to the emitter of the transistor.
Tech Tip: Recall that DC bias is used to set the operation point of the transistor. The voltages established by resistors R1, R2, and R3 set the quiescent (no signal) operating point for the transistor. In this example, the values are chosen so that approximately half of the source voltage is present at the junction of R3 and the transistor’s collector. Note that the DC bias is independent of C1, C2, C3, and C4. These components are involved with the dynamic (AC) performance of the amplifier.
The importance of feedback
Feedback and gain are the central concepts at play in this discussion. As suggested in Figure 2, the emitter bypass capacitor (C2 in Figure 1) directly impacts both parameters.
Definition of feedback
Negative feedback has a profound impact on an amplifier performance. Feedback makes an amplifier more linear (improved fidelity), more stable, increases the bandwidth, and reduces the amplifier’s noise. This improved performance comes at the cost of gain. As suggested in Figure 2, the lower gain (high feedback) configuration will provide the best fidelity.
Tech Tip As a design exercise you are encouraged to measure the performance using a total harmonic distortion meter or the simple procedure outlined here. Observe that the measurement begins with a low distortion signal source such as the Wien bridge oscillator.
Feedback mechanism in a common emitter amplifier
Negative feedback is typically explored through the lens of the op amp or control system such as the PID. In both cases we can easily identify the physical feedback wire where the output signal is fed back to the input.
The feedback mechanism for the common emitter amplifier is subtle, as there is no physical wire. Instead, we need to think about this in terms of current and voltages. For the sake of conversation:
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assume that our transistor’s output signal is defined as the collector current.
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note that the collector current is coupled (fed back) to the emitter.
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note that the transistor’s base if effectively nailed to the DC bias voltage by R1 and R2
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momentarily remove the bypass capacitor C2
To understand the feedback mechanism, consider what happens when the collector current is increased. The collector current is coupled to the emitter current, causing a corresponding rise in R4’s voltage. When we consider the fixed R1 and R2 bias voltage, the transistor’s increased current is met with a tendency to turn itself off. This property is known as degenerative feedback.
At this point we can consider the operation of the bypass capacitor C2. When installed, this capacitor breaks the feedback mechanism. It effectively nails (AC grounds) the emitter voltage to the emitter quiescent voltage. Since the voltage on R4 is steady the feedback mechanism is disabled.
Tech Tip: The previous statement about disabling the feedback mechanism is oversimplified as it does not account for the transistor’s intrinsic emitter resistance. This internal resistor, affectionately known as little r_e, is a function of temperature and emitter current. It is calculated as:
r_e = \dfrac{25 mV}{I_E} Where 25 mV is the semiconductor’s thermal voltage.
Perhaps another day we can explore this important calculation and the implication for transistor gain. For now, know that r_e in an important part of the mechanism that establishes the limit of amplifier gain.
Why do we need the emitter resistor?
In an ideal setting we could eliminate the emitter resistor. However, in the real world we quickly discover that not all transistors are equal. For example, the DC gain parameter (H_{FE}) for a 2N3904BU operating at 10 mA can vary from 100 to 300. The gain is also influenced by temperature.
The emitter resistor provides a feedback mechanism to mitigate the variations in individual transistors and to mitigate changes in temperature. This is a self-regulating feedback mechanism to stabilize the transistor.
Note that this DC feedback mechanism is related to the dynamic AC feedback. However, they are not same, as will be shown in the next section.
What is the recommended size of the emitter bypass capacitor?
As a starting point, the emitter bypass capacitor should have 1/10 the reactance of the emitter resistor for the lowest frequency of interest. For example, suppose the circuit in Figure 1 serves an audio amplifier with a 20 Hz cutoff frequency. We calculate the capacitor value as:
X_C = \dfrac{1}{2\pi fC} = 14 = \dfrac{1}{2 \pi 20 C}
The resulting capacitance is about 470 uF.
Figures 3 and 4 show the frequency response for the amplifier when the bypass capacitor is set to 100 and 1 uF respectively. For Figure 3, the 100 uF capacitor is sufficient resulting in an amplifier with a relatively flat 16 dB passband. Figure 4 shows what happens when the capacitor is too small. The amplifier has the same 16 dB response for higher frequencies. However, on the “front porch” the gain is about 10 dB. In many respects, this is a restatement of Figure 2. Recall that the gain of the amplifier is determined by the amount of emitter resistor bypassed by the emitter capacitor. At low frequencies, the reactance of the 1 uF capacitance to too high. In fact, for low frequencies, the capacitor may as well be absent. It is only when we approach 10 kHz that the bypass capacitor becomes effective.
Figure 3: Frequency response of the amplifier when R4 is set to 50% and C2 is set to 100 uF.
Figure 4: Frequency response of the amplifier when R4 is set to 50% and C2 is set to 1 uF.
In the previous section we stated that the feedback mechanism for the DC bias and the dynamic AC were related but different. This is clearly shown in Figure 4. For low frequencies, the emitter bypass capacitor is not effective. In fact, for steady-state DC condition, the emitter bypass capacitor is invisible. Consequently, we can state that the DC characteristics and AC characteristics are not the same. Yet, they both operate using the same self-regulating mechanism based on the current passing through the transistor.
Note that the observed high-pass filter action in the first decade of Figure 4 is caused by the limitations of the input and output coupling capacitors. For improved performance a more complex DC coupled circuit is required.
Parting thoughts
The emitter bypass capacitor is one of several devices that determines the gain for the stage. The CE amplifier operates using the principle of negative feedback. Unlike the op amp, there is no “feedback wire.” Instead, the feedback takes the form of the current passing through the transistor. As the transistor is turned on, there is a counteraction (negative) response as voltage developed across the emitter resistor tends to turn off the transistor. The emitter bypass capacitor provides limited ability to adjust the amount of feedback where a fully bypassed emitter resistor yields the highest gain. We recognize the importance of capacitive reactance as the bypass capacitor “kicks in” when this reactance is low relative to the emitter resistor.
Please provide a thumbs up if you found this content useful. Also, please let us know if you would like to explore related topics. Finally, be sure to test you circuit knowledge by answering the questions at the end of this note.
Best wishes,
APDahlen
About this author
Aaron Dahlen, LCDR USCG (Ret.), serves as an application engineer at DigiKey. He has a unique electronics and automation foundation built over a 27-year military career as a technician and engineer which was further enhanced by 12 years of teaching (partially interwoven with military experience). With an MSEE degree from Minnesota State University, Mankato, Dahlen has taught in an ABET-accredited EE program, served as the program coordinator for an EET program, and taught component-level repair to military electronics technicians. Dahlen has returned to his Northern Minnesota home and thoroughly enjoys researching and writing educational articles about electronics and automation.
Highlighted Experience
Dahlen is an active contributor to the DigiKey TechForum. At the time of this writing, he has created over 150 unique posts and provided an additional 500 forum posts. Dahlen shares his insights on a wide variety of topics including microcontrollers, FPGA programming in Verilog, and a large body of work on industrial controls.
Questions
The following questions will help reinforce the content of the article.
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What are the properties of the CE amplifier and how does it differ from the CC amplifier?
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Why does the CE amplifier require an emitter resistor?
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What amplifier aspects are improved by the application of negative feedback?
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With regards to the common emitter amplifier, identify the functional equivalent of the “feedback wire.”
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What is the purpose of R4 as shown in Figure 1?
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Explain this statement mathematically, “, for steady-state DC condition, the emitter bypass capacitor is invisible.”
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Sketch Figure 4: identify and then describe the section(s) associated with the emitter bypass capacitor operation or lack of operation.
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What is capacitive reactance?
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Explain the slang terms “nailed to the bias voltage” and “AC ground”.
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What is the rule of thumb for selecting the value of the emitter bypass capacitor?
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Estimate the steady-state bias voltage on the base of the transistor. Hint: As an estimate, you may ignore the base current.
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Explain why Figure 2 represents a nonlinear response. Hint: The answer should focus on the relationship between the curves, not the distortion at maximum gain.
Critical thinking questions
These critical thinking questions expand the article’s content allowing you to develop a big picture understanding the material and its relationship to adjacent topics. They are often open ended, require research, and are best answered in essay form.
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What is meant by the term “DC coupled” amplifier?
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There are four capacitors in Figure 1. Identify the type of filter associated with each capacitor. Hint: The term “Miller” is associated with one of the capacitors.
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Describe the result and utility of an amplifier where R_C and R_E are equal. Do not use the emitter bypass capacitor. Hint: Consider the two wires from a microphone using a XLR connector. Also consider the relationship to CMRR.
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What is the difference between a 16 dB voltage gain and a 16 dB power gain? Assuming a common output resistance express you answer in terms of power.