How does a differential amplifier reject common-mode signals?
2 Answers
A differential amplifier is designed to amplify the difference between two input signals while rejecting any signals common to both inputs. This ability to reject common-mode signals (i.e., signals that are present on both inputs) is crucial in many applications, such as audio systems, communication devices, and sensor interfaces, where noise or interference may affect both inputs equally.
### Key Concepts: Differential and Common-Mode Signals
- **Differential Signal**: The difference between two input signals, often referred to as \(V_d = V_1 - V_2\), where \(V_1\) and \(V_2\) are the input voltages.
- **Common-Mode Signal**: A signal that is present on both input lines equally. This can be represented as \(V_{cm} = (V_1 + V_2)/2\). It often comes from external noise sources like electromagnetic interference (EMI).
### How the Differential Amplifier Works
A differential amplifier typically has two inputs, and its output is based on the voltage difference between them. Let's break down how it rejects common-mode signals:
1. **Balanced Inputs**: The differential amplifier has two identical inputs, meaning it processes both input signals symmetrically. This balanced design is key to rejecting common-mode signals.
2. **Common-Mode Rejection Ratio (CMRR)**: The ability of a differential amplifier to reject common-mode signals is quantified by the **Common-Mode Rejection Ratio** (CMRR). A higher CMRR indicates better performance in rejecting common-mode signals. CMRR is defined as:
\[
\text{CMRR} = 20 \log_{10} \left( \frac{\text{Differential Gain}}{\text{Common-Mode Gain}} \right)
\]
A good differential amplifier has a very high differential gain and very low common-mode gain, meaning it will significantly amplify the difference between \(V_1\) and \(V_2\) (the differential signal) while almost ignoring any common signal.
3. **Subtraction of Inputs**: A differential amplifier amplifies only the difference between the two inputs:
\[
V_{out} = A_d \times (V_1 - V_2)
\]
Where:
- \(V_{out}\) is the output voltage,
- \(A_d\) is the differential gain,
- \(V_1\) and \(V_2\) are the input voltages.
For common-mode signals, since both \(V_1\) and \(V_2\) are the same (or nearly the same), their difference will be close to zero. Thus, the output due to the common-mode signal is greatly reduced, ideally to zero.
4. **Active Devices (Transistors/Op-Amps)**: In practical circuits, transistors or operational amplifiers (op-amps) are used. These devices have internal mechanisms to suppress common-mode signals. For example:
- **Emitter-Coupled Transistors**: In a differential pair using bipolar junction transistors (BJTs), the common emitter node acts as a reference point. If a common-mode signal appears at both bases (inputs), it affects both transistors equally, resulting in no change in the output current difference.
- **Op-Amp-Based Differential Amplifier**: Operational amplifiers are used with feedback resistors to implement precise differential gain while minimizing the effect of common-mode signals.
### Factors Affecting Common-Mode Rejection
Several factors can influence the effectiveness of a differential amplifier’s common-mode rejection:
- **Mismatch in Components**: In real circuits, slight mismatches in resistors or transistor parameters can reduce the CMRR, making the amplifier more sensitive to common-mode signals.
- **Power Supply Noise**: If the power supply is noisy and the noise is coupled into both inputs, it may appear as a common-mode signal. A differential amplifier with a high CMRR can effectively reject this noise.
- **Frequency Dependence**: CMRR is often frequency-dependent. At low frequencies, the CMRR is typically higher, but at higher frequencies (due to parasitic capacitances and other non-ideal effects), the CMRR may degrade.
### Example of Common-Mode Signal Rejection
Suppose the input signals are:
- \(V_1 = 1 \, \text{V} + 100 \, \text{mV (noise)}\)
- \(V_2 = 0 \, \text{V} + 100 \, \mV (same noise)}\)
Here, the common-mode signal is 100 mV of noise, which is the same on both inputs. The differential amplifier will subtract these two signals:
\[
V_d = (1 + 0.1) \, \text{V} - (0 + 0.1) \, \text{V} = 1 \, \text{V}
\]
The noise (100 mV) cancels out, and the amplifier only amplifies the difference between the signals (1 V), rejecting the common-mode noise.
### Conclusion
A differential amplifier rejects common-mode signals by utilizing its ability to amplify only the difference between two input signals while canceling out signals that are common to both. This rejection is primarily achieved through the balanced circuit design and can be measured by the Common-Mode Rejection Ratio (CMRR). With high CMRR, differential amplifiers can effectively reduce the impact of external noise, making them ideal for precision signal processing applications.
### Key Concepts: Differential and Common-Mode Signals
- **Differential Signal**: The difference between two input signals, often referred to as \(V_d = V_1 - V_2\), where \(V_1\) and \(V_2\) are the input voltages.
- **Common-Mode Signal**: A signal that is present on both input lines equally. This can be represented as \(V_{cm} = (V_1 + V_2)/2\). It often comes from external noise sources like electromagnetic interference (EMI).
### How the Differential Amplifier Works
A differential amplifier typically has two inputs, and its output is based on the voltage difference between them. Let's break down how it rejects common-mode signals:
1. **Balanced Inputs**: The differential amplifier has two identical inputs, meaning it processes both input signals symmetrically. This balanced design is key to rejecting common-mode signals.
2. **Common-Mode Rejection Ratio (CMRR)**: The ability of a differential amplifier to reject common-mode signals is quantified by the **Common-Mode Rejection Ratio** (CMRR). A higher CMRR indicates better performance in rejecting common-mode signals. CMRR is defined as:
\[
\text{CMRR} = 20 \log_{10} \left( \frac{\text{Differential Gain}}{\text{Common-Mode Gain}} \right)
\]
A good differential amplifier has a very high differential gain and very low common-mode gain, meaning it will significantly amplify the difference between \(V_1\) and \(V_2\) (the differential signal) while almost ignoring any common signal.
3. **Subtraction of Inputs**: A differential amplifier amplifies only the difference between the two inputs:
\[
V_{out} = A_d \times (V_1 - V_2)
\]
Where:
- \(V_{out}\) is the output voltage,
- \(A_d\) is the differential gain,
- \(V_1\) and \(V_2\) are the input voltages.
For common-mode signals, since both \(V_1\) and \(V_2\) are the same (or nearly the same), their difference will be close to zero. Thus, the output due to the common-mode signal is greatly reduced, ideally to zero.
4. **Active Devices (Transistors/Op-Amps)**: In practical circuits, transistors or operational amplifiers (op-amps) are used. These devices have internal mechanisms to suppress common-mode signals. For example:
- **Emitter-Coupled Transistors**: In a differential pair using bipolar junction transistors (BJTs), the common emitter node acts as a reference point. If a common-mode signal appears at both bases (inputs), it affects both transistors equally, resulting in no change in the output current difference.
- **Op-Amp-Based Differential Amplifier**: Operational amplifiers are used with feedback resistors to implement precise differential gain while minimizing the effect of common-mode signals.
### Factors Affecting Common-Mode Rejection
Several factors can influence the effectiveness of a differential amplifier’s common-mode rejection:
- **Mismatch in Components**: In real circuits, slight mismatches in resistors or transistor parameters can reduce the CMRR, making the amplifier more sensitive to common-mode signals.
- **Power Supply Noise**: If the power supply is noisy and the noise is coupled into both inputs, it may appear as a common-mode signal. A differential amplifier with a high CMRR can effectively reject this noise.
- **Frequency Dependence**: CMRR is often frequency-dependent. At low frequencies, the CMRR is typically higher, but at higher frequencies (due to parasitic capacitances and other non-ideal effects), the CMRR may degrade.
### Example of Common-Mode Signal Rejection
Suppose the input signals are:
- \(V_1 = 1 \, \text{V} + 100 \, \text{mV (noise)}\)
- \(V_2 = 0 \, \text{V} + 100 \, \mV (same noise)}\)
Here, the common-mode signal is 100 mV of noise, which is the same on both inputs. The differential amplifier will subtract these two signals:
\[
V_d = (1 + 0.1) \, \text{V} - (0 + 0.1) \, \text{V} = 1 \, \text{V}
\]
The noise (100 mV) cancels out, and the amplifier only amplifies the difference between the signals (1 V), rejecting the common-mode noise.
### Conclusion
A differential amplifier rejects common-mode signals by utilizing its ability to amplify only the difference between two input signals while canceling out signals that are common to both. This rejection is primarily achieved through the balanced circuit design and can be measured by the Common-Mode Rejection Ratio (CMRR). With high CMRR, differential amplifiers can effectively reduce the impact of external noise, making them ideal for precision signal processing applications.
A differential amplifier rejects common-mode signals through its design, which specifically aims to amplify the difference between two input signals while minimizing the effects of signals common to both inputs. Here's how it works in detail:
### **1. Differential Input Structure**
A differential amplifier has two inputs: the inverting input (−) and the non-inverting input (+). It is designed to amplify only the voltage difference between these two inputs.
### **2. Common-Mode Rejection**
Common-mode signals are those that appear equally on both the inverting and non-inverting inputs. The differential amplifier is built to have high Common-Mode Rejection Ratio (CMRR), which measures its ability to reject common-mode signals.
### **3. Amplifier Configuration**
The basic configuration of a differential amplifier involves two matched transistors or operational amplifier stages, each connected to one of the inputs. Here’s how it works:
- **Input Stage**: The differential amplifier consists of two inputs connected to a pair of transistors (in the case of a transistor-based differential amplifier) or a pair of input terminals in an operational amplifier. These transistors or stages are designed to balance out the common-mode signals.
- **Differential Gain**: The output is proportional to the difference between the two input voltages. Mathematically, the output \( V_{out} \) is given by:
\[
V_{out} = A_d (V_{in+} - V_{in-})
\]
where \( A_d \) is the differential gain, \( V_{in+} \) is the voltage at the non-inverting input, and \( V_{in-} \) is the voltage at the inverting input.
- **Common-Mode Signal Handling**: When a common-mode signal \( V_{CM} \) is present, it affects both inputs equally. Ideally, this signal should not affect the differential output, but real-world amplifiers are not perfect. The degree to which common-mode signals are rejected is quantified by the CMRR.
### **4. Common-Mode Rejection Ratio (CMRR)**
CMRR is a critical parameter that indicates how well the amplifier can reject common-mode signals compared to differential signals. It is defined as:
\[
\text{CMRR} = \frac{A_{d}}{A_{CM}}
\]
where \( A_{d} \) is the differential gain and \( A_{CM} \) is the common-mode gain.
In an ideal differential amplifier, \( A_{CM} \) is zero, which means the CMRR is infinite. In practice, the CMRR is very high, meaning that the amplifier significantly attenuates any common-mode signals.
### **5. Practical Implementation**
In practical implementations, additional techniques are used to improve common-mode rejection:
- **Matched Components**: Ensuring that the transistors or operational amplifier stages are well-matched helps in rejecting common-mode signals.
- **Feedback Networks**: Using feedback networks can help stabilize the gain and further reduce common-mode effects.
- **Shielding and Grounding**: Proper shielding and grounding practices help minimize the pickup of common-mode noise.
In summary, a differential amplifier rejects common-mode signals by design, focusing on amplifying only the difference between two input signals while ideally ignoring signals that are common to both. This characteristic is quantified by the CMRR and is crucial for accurate signal processing in various applications.
### **1. Differential Input Structure**
A differential amplifier has two inputs: the inverting input (−) and the non-inverting input (+). It is designed to amplify only the voltage difference between these two inputs.
### **2. Common-Mode Rejection**
Common-mode signals are those that appear equally on both the inverting and non-inverting inputs. The differential amplifier is built to have high Common-Mode Rejection Ratio (CMRR), which measures its ability to reject common-mode signals.
### **3. Amplifier Configuration**
The basic configuration of a differential amplifier involves two matched transistors or operational amplifier stages, each connected to one of the inputs. Here’s how it works:
- **Input Stage**: The differential amplifier consists of two inputs connected to a pair of transistors (in the case of a transistor-based differential amplifier) or a pair of input terminals in an operational amplifier. These transistors or stages are designed to balance out the common-mode signals.
- **Differential Gain**: The output is proportional to the difference between the two input voltages. Mathematically, the output \( V_{out} \) is given by:
\[
V_{out} = A_d (V_{in+} - V_{in-})
\]
where \( A_d \) is the differential gain, \( V_{in+} \) is the voltage at the non-inverting input, and \( V_{in-} \) is the voltage at the inverting input.
- **Common-Mode Signal Handling**: When a common-mode signal \( V_{CM} \) is present, it affects both inputs equally. Ideally, this signal should not affect the differential output, but real-world amplifiers are not perfect. The degree to which common-mode signals are rejected is quantified by the CMRR.
### **4. Common-Mode Rejection Ratio (CMRR)**
CMRR is a critical parameter that indicates how well the amplifier can reject common-mode signals compared to differential signals. It is defined as:
\[
\text{CMRR} = \frac{A_{d}}{A_{CM}}
\]
where \( A_{d} \) is the differential gain and \( A_{CM} \) is the common-mode gain.
In an ideal differential amplifier, \( A_{CM} \) is zero, which means the CMRR is infinite. In practice, the CMRR is very high, meaning that the amplifier significantly attenuates any common-mode signals.
### **5. Practical Implementation**
In practical implementations, additional techniques are used to improve common-mode rejection:
- **Matched Components**: Ensuring that the transistors or operational amplifier stages are well-matched helps in rejecting common-mode signals.
- **Feedback Networks**: Using feedback networks can help stabilize the gain and further reduce common-mode effects.
- **Shielding and Grounding**: Proper shielding and grounding practices help minimize the pickup of common-mode noise.
In summary, a differential amplifier rejects common-mode signals by design, focusing on amplifying only the difference between two input signals while ideally ignoring signals that are common to both. This characteristic is quantified by the CMRR and is crucial for accurate signal processing in various applications.