Feedback Amplifiers
Feedback Amplifier: The feedback amplifier can be defined as an amplifier which has
a feedback path that exists between output and input. In this type of amplifier, the output
signal is sampled, then fed back to the input where it is mixed with the original source
signal to give the input signal, which is then amplified and turned into the output signal.
This is how the feedback process takes place in a feedback amplifier.
Two Types of Feedback Amplifier:
1. Positive Feedback Amplifier- Positive feedback can be defined as when the feedback
current, otherwise voltage, is applied with the purpose of increasing the input voltage.
Direct feedback is another name for this positive feedback. Because positive feedback
generates unnecessary distortion, it is often not used in amplifiers. But since it amplifies
the original signal power, it can be used in oscillator circuits.
2. Negative Feedback Amplifier- Negative feedback can be defined as when the feedback
current, otherwise voltage, is applied with the purpose of reducing the amplifier input.
Inverse feedback is another name for this negative feedback. This kind of feedback is
commonly used in amplifier circuits.
Here,
𝑥
𝐴 = 𝑜 = Gain of Basic Amplifier
𝛽=
𝑥𝑖
𝑥𝑓
= Feedback Factor
𝑥𝑜
𝑥𝑜
𝐴𝑓 =
𝑥𝑠
= Gain with Feedback
𝑥𝑖 = 𝑥𝑠 − 𝑥𝑓
= 𝑥𝑠 − 𝛽𝑥𝑜
= 𝑥𝑠 − 𝛽𝐴𝑥𝑖
⇒ 𝑥𝑖 (1 + 𝐴𝛽) = 𝑥𝑠
∴ 𝐴𝑓 =
𝑥𝑜
𝑥𝑜
𝐴
=
=
<𝐴
𝑥𝑠 𝑥𝑖 (1 + 𝐴𝛽) 1 + 𝐴𝛽
𝐴 > 𝐴𝑓
Gain with Feedback is always smaller than Gain of Basic Amplifier.
(1 + 𝐴𝛽) → Amount of Feedback
If, 𝐴𝛽 >> 1
∴ 𝐴𝑓 =
𝑥𝑜
𝐴
𝐴
1
=
≅
=
𝑥𝑠 1 + 𝐴𝛽 𝐴𝛽 𝛽
Now, Gain of Feedback Amplifier is independent of Gain of Basic Amplifier; Gain of
Feedback Amplifier depends only on feedback factor.
Feedback factor (𝛽) is not affected much by temperature, as 𝛽 is the ratio of resistors.
Moreover, they will cancel each other out at higher temperatures. So, ultimately 𝐴𝑓 (Gain
with Feedback) does not change, and instead gets more stable.
Advantages of Negative Feedback Amplifier:
➔ Stabilizes Gain
➔ Widens Bandwidth
➔ Reduces Noise
➔ Reduces Non-Linear Distortion
➔ Adjusts Input/Output Resistance
Feedback Topologies:
1. Sampling voltage at output; Mixing voltage at input; Voltage Sampling & Voltage
Mixing.
𝑥𝑠 = 𝑉𝑠 , 𝑥𝑖 = 𝑉𝑖 , 𝑥𝑜 = 𝑉𝑜 ;
𝑉
𝐴 = 𝑜 → Voltage Amplifier
𝑉𝑖
2. Sampling voltage at output; Mixing current at input; Voltage Sampling & Current
Mixing.
𝑥𝑠 = 𝐼𝑠 , 𝑥𝑖 = 𝐼𝑖 , 𝑥𝑜 = 𝑉𝑜 ;
𝑉
𝐴 = 𝑜 → Transresistance Amplifier
𝐼𝑖
3. Sampling current at output; Mixing current at input; Current Sampling & Current
Mixing.
𝑥𝑠 = 𝐼𝑠 , 𝑥𝑖 = 𝐼𝑖 , 𝑥𝑜 = 𝐼𝑜 ;
𝐼
𝐴 = 𝑜 → Current Amplifier
𝐼𝑖
4. Sampling current at output; Mixing voltage at input; Current Sampling & Voltage
Mixing.
𝑥𝑠 = 𝑉𝑠 , 𝑥𝑖 = 𝑉𝑖 , 𝑥𝑜 = 𝐼𝑜 ;
𝐼
𝐴 = 𝑜 → Transconductance Amplifier
𝑉𝑖
1. Voltage Sampling, Voltage Mixing (Series-Shunt Feedback Amplifier)
Block Diagram:
Input: Series Connection
Output: Shunt Connection
𝑉
𝐴𝑓 = 𝑜 = Gain with Feedback
𝑉𝑠
𝑅𝑖𝑓 = Input Resistance of Feedback Amplifier
𝑅𝑜𝑓 = Output Resistance of Feedback Amplifier
𝐴=
𝑉𝑜
𝑉𝑖
𝑉𝑠 = 𝑉𝑖 + 𝑉𝑓
= 𝑉𝑖 + 𝛽𝑉𝑜
= 𝑉𝑖 + 𝛽𝐴𝑉𝑖
= 𝑉𝑖 (1 + 𝐴𝛽)
𝑉
𝑉𝑜
𝑉𝑠
𝑉𝑖 (1+𝐴𝛽)
∴ 𝐴𝑓 = 𝑜 =
𝑅𝑖𝑓 =
=
𝐴
1+𝐴𝛽
𝑉
[Gain, 𝐴 = 𝑜]
𝑉𝑖
𝑉𝑖 (1 + 𝐴𝛽)
𝐼𝑖
= 𝑅𝑖 (1 + 𝐴𝛽)
# In order to find the output resistance, we apply a test voltage 𝑉𝑥 . We will also set 𝑉𝑠 to
be zero, otherwise 𝑅𝑜𝑓 =
𝑉𝑥
𝐼𝑥
will not be valid as there will be current from 𝑉𝑠 as well.
# The current to the feedback network is zero because of high input resistance considering
the ideal case.
𝑉𝑥 = 𝐼𝑥 𝑅𝑜 + 𝐴𝑉𝑖
= 𝐼𝑥 𝑅𝑜 − 𝐴𝑉𝑓
= 𝐼𝑥 𝑅𝑜 − 𝐴𝛽𝑉𝑥
∴ 𝐼𝑥 𝑅𝑜 = 𝑉𝑥 (1 + 𝐴𝛽)
∴ 𝑅𝑜𝑓 =
𝑉𝑜 = 𝑉𝑖 + 𝑉𝑓
⇒ 𝑉𝑖 = −𝑉𝑓 [𝑉𝑠 → 0]
𝑉𝑥
𝑅𝑜
=
𝐼𝑥 1 + 𝐴𝛽
# In series connection, resistance increases by factor of (1 + 𝐴𝛽) whether at input or
output.
# In parallel/shunt connection, resistance decreases by factor of (1 + 𝐴𝛽).
2. Voltage Sampling, Current Mixing (Shunt-Shunt Feedback Amplifier)
Block Diagram:
Here,
𝑉
𝐴𝑓 = 𝑜 = Gain of Feedback Amplifier
𝐼𝑠
𝑉
𝐴 = 𝑜 = Gain of Basic Amplifier = Transresistance Gain
𝐼𝑖
𝑅𝑖𝑓 = Input Resistance of Feedback Amplifier
𝑅𝑜𝑓 = Output Resistance of Feedback Amplifier
𝐼𝑠 = 𝐼𝑖 + 𝐼𝑓
= 𝐼𝑖 + 𝛽𝑉𝑜
= 𝐼𝑖 + 𝛽𝐴𝐼𝑖
= 𝐼𝑖 (1 + 𝐴𝛽)
∴ 𝐴𝑓 =
𝑅𝑖𝑓 =
𝑉𝑜
𝑉𝑜
𝐴
=
=
𝐼𝑠 𝐼𝑖 (1 + 𝐴𝛽) 1 + 𝐴𝛽
𝑉𝑖
𝑉𝑖
𝑅𝑖
=
=
𝐼𝑠 𝐼𝑖 (1 + 𝐴𝛽) 1 + 𝐴𝛽
# Here, the connection is shunt, so resistance decreases by factor of (1 + 𝐴𝛽).
# In order to find 𝑅𝑜𝑓 , we apply a test voltage 𝑉𝑥 once again, and set 𝐼𝑠 to zero, under the
assumption that current flowing to the feedback network is zero due to ideal conditions.
𝑉𝑥 → Active; 𝐼𝑠 = 0
𝐼𝑠 = 𝐼𝑖 + 𝐼𝑓
𝐼𝑖 = −𝐼𝑓
∴ 𝑉𝑥 = 𝐼𝑥 𝑅𝑜 + 𝐴𝐼𝑖
= 𝐼𝑥 𝑅𝑜 − 𝐴𝐼𝑓
= 𝐼𝑥 𝑅𝑜 − 𝐴𝛽𝑉𝑥
∴ 𝐼𝑥 𝑅𝑜 = 𝑉𝑥 (1 + 𝐴𝛽)
∴ 𝑅𝑜𝑓 =
𝑉𝑥
𝑅𝑜
=
𝐼𝑥 1 + 𝐴𝛽
3. Current Sampling, Current Mixing (Shunt-Series Feedback Amplifier)
Block Diagram:
Here,
𝐼
𝐴
𝐼𝑠
𝐼𝑜
1+𝐴𝛽
𝐴𝑓 = 𝑜 =
𝐴=
𝐼𝑖
𝑅𝑖𝑓 =
= Current Gain
𝑅𝑖
1+𝐴𝛽
𝑅𝑜𝑓 = 𝑅𝑜 (1 + 𝐴𝛽)
4. Current Sampling, Voltage Mixing (Series-Series Feedback Amplifier)
Block Diagram:
Here,
𝐼
𝐴
𝑉𝑠
1+𝐴𝛽
𝐴𝑓 = 𝑜 =
𝐼
𝐴 = 𝑜 = Transconductance Gain
𝑉𝑖
𝑅𝑖𝑓 = 𝑅𝑖 (1 + 𝐴𝛽)
𝑅𝑜𝑓 = 𝑅𝑜 (1 + 𝐴𝛽)
Basic Amplifier
Applying Voltage Divider Rule:
𝑅
𝑉𝑓 =
𝛽=
𝑅+𝑅𝑓
𝑉𝑓
𝑉𝑜
𝐴𝑓 =
=
𝑉𝑜 ;
𝑅
𝑅+𝑅𝑓
𝑅𝑓
1
=1+
𝛽
𝑅
𝑅𝑖𝑓 = 𝑅𝑖𝑑 (1 + 𝐴𝛽)
𝑅𝑜𝑓 =
𝑅𝑜
1 + 𝐴𝑂𝐿 𝛽
𝑉
𝐴𝑂𝐿
𝑉𝑖
1+𝐴𝑂𝐿 𝛽
𝐴𝑓 = 𝑜 =
=
𝐴𝑂𝐿
𝐴𝑂𝐿 𝛽
=
1
𝛽
[𝐴𝑂𝐿 𝛽 >> 1]