Unit 3: Feedback Amplifiers PDF

## Unit 3: Feedback Amplifiers - **Feedback Amplifier:** A circuit where the output signal is sampled and fed back to the input signal. - The feedback process alters the performance of the amplifier, including the input impedance, current gain, voltage gain, and bandwidth. - **Basic Concept of Feed...

## Unit 3: Feedback Amplifiers - **Feedback Amplifier:** A circuit where the output signal is sampled and fed back to the input signal. - The feedback process alters the performance of the amplifier, including the input impedance, current gain, voltage gain, and bandwidth. - **Basic Concept of Feedback:** - A block diagram of an amplifier with feedback is shown below: - **Diagram Description:** - The diagram shows a basic amplifier with input signal (Vi), output signal (Vo), feedback network, sampling network, and mixer. - The output quantity (voltage or current) is sampled by a suitable sampler, which can be either a voltage sampler or a current sampler. - The sampled output signal is then fed back to the feedback network. - This feedback network combines the external source signal (Vs) and the output signal (Vo) through a mixer, which is fed back to the basic amplifier. - This kind of mixer is known as a "comparator" and is commonly implemented as a series mixer or a shunt mixer. - **Basic Amplifier Parameters:** - **A**: Gain of the basic amplifier. - **β**: Feedback ratio, (also known as feedback factor). - **Af**: Gain of the feedback amplifier. - **Vs**: Source voltage. - **Is**: Source current. - **Vf**: Feedback signal (can be current or voltage). - **Types of Feedback:** - **Positive Feedback:** Feedback signal in phase with the source signal. - Increases gain exponentially. - Also known as **regenerative feedback**. - Amplifier gain with positive feedback: - $Af = \frac{Vo}{Vs}=\frac{Vo}{V_i-Vf}=\dfrac{\frac{Vo}{V_i}}{1-\frac{Vf}{V_i}}=\frac{A}{1-\beta}$ - **Here (|Af| > |A|)**. - **Advantages:** - Increases gain. - **Disadvantages:** - Decreases bandwidth. - Increases distortion and noise. - Increases instability of the amplifier. - **Applications:** - Oscillators. - **Negative Feedback:** Feedback signal out of phase with the source signal. - Reduces gain. - Also known as **degenerative feedback**. - Amplifier gain with negative feedback: - $Af = \frac{Vo}{Vs} =\frac {Vo}{V_i+Vf}=\frac{\frac {Vo}{V_i}}{1+\frac{Vf}{V_i}}=\frac{A}{1+A\beta}$ - **Here (|Af| < |A|)**. - **Advantages:** - Stabilizes gain. - Increases the bandwidth. - Decreases distortion and noise. - Modifies input and output impedances. - **Disadvantages:** - Reduces gain. - **Feedback Network:** - It samples a portion of the output signal and feeds it to the input mixer. - This network can include resistors, capacitors, and inductors. - **Loop Gain (Aβ):** - Used to describe the effect of feedback. - It's the product of the voltage gain (A) and the feedback factor (β). - **Feedback gain (dB):** - $dB = 20 \log A_f=20 \log \frac{A}{1+AB}$ - $dB = 20 \log \frac{1}{1+AB}$ - **Topologies of Feedback Amplifiers:** - **Types of feedback amplifier:** - The output signal sampled can be either voltage or current. - The sampled signal can be mixed either in series or in shunt with the input signal. - Based on the type of sampling at the output side and the type of mixing at the input side, we can categorize feedback amplifiers into four categories. - **1. Voltage Series Feedback Amplifier:** (also called Series Shunt Feedback Amplifier) - Output signal sampled is voltage and the mixing is in series. - Input impedance (Z_i) or R increases due to series mixing (voltage), while output impedance decreases due to shunt sampling (mixing). - **2. Current Series Feedback Amplifier:** (also called Series Series) - Output signal sampled is current and the mixing is in series. - Output parameter monitored is current. - Input impedance increases due to series mixing. - This is also called transconductance amplifier. - Transconductance without feedback: - $G_m = \frac{I_o}{V_i}$ - Transconductance with feedback: - $G_m_f = \frac{I_o}{V_s} = \frac{I_o}{V_i+V_f}=\frac{I_o}{V_i+\beta I_o} = \frac{\frac{I_o}{V_i}}{1+B\frac{I_o}{V_i}}=\frac{G_m}{(1+\beta G_m)}$ - Input impedance without feedback: - $R_i = \frac{V_i}{I_s}$. - Input impedance with feedback: - $R_{if} = \frac{V_s}{I_s} = \frac{V_i+V_f}{I_s} = \frac{V_i+\beta I_o}{I_s} = \frac{V_i}{I_s}+\frac{\beta I_o}{I_s} R_i = R_i + \beta R_i G_m = R_ί (1+\beta G_m)$. - Output impedance: - Output impedance can be obtained by equating Vs = 0 and applying voltage V at the output. - Then the ratio of applied voltage to the resultant current is known as the output impedance. - $Z_o = \frac{V}{I} = \frac{G_mV_i}{I} = \frac{G_mV_i}{I}=\frac{G_mV_i}{-G_mV_f}$ - **3. Current Shunt Feedback Amplifier:** (also called Shunt Series Feedback Amplifier) - Output signal sampled is current and the mixing is in shunt.. - Output parameter monitored is current. - Input impedance increases with feedback due to series mixing. - **4. Voltage Shunt Feedback Amplifier:** (also called Transresistance Amplifier) - Output signal sampled is voltage and the mixing is in shunt. - Output parameter monitored is voltage. - Input impedance increases due to series mixing. - Input impedance without feedback: - $R_m = \frac{V_o}{I_s}$. - Input impedance with feedback: - $R_{mf} = \frac {V_o}{I_s}=\frac {V_o}{I_i+I_F}=\frac{V_o}{I_i + \beta V_o}=\frac {\frac{V_o}{I_i}}{1+\beta \frac{V_o}{I_i}}=\frac{R_m}{(1+\beta R_m)}$ - Output impedance: - $R_{of}=\frac {V}{I}=\frac {IR_o + R_mI_f}{I}=R_o+R_m I_f= R_o+R_m \beta V_o=R_o(1+\beta R_m)$ - **Effect of Negative Feedback on Amplifier Characteristics:** - **1. Increased Stability (Stabilization of Gain):** - The voltage gain due to negative feedback is given by: - $Af = \frac{A}{1+A\beta}$. - **Where:** - **A:** Voltage gain without feedback. - **β:** The feedback factor. - The gain is reduced by a factor of 1+Aβ. - **If Aβ>>1, then Af = 1/β**. This means that amplifier gain depends only on the feedback network. - This stabilization prevents issues like aging of transistors or replacement of transistors with different values of β. - **2. Desensitivity of Transfer Gain:** - **Sensitivity:** Fractional change in amplifier voltage gain with feedback divided by the fractional change in the voltage gain without feedback. - **Sensitivity** - $Sensitivity = \frac{1}{1+A\beta}$. - **Desensitivity:** Reciprocal of sensitivity. - $Desensitivity = 1+A\beta$ - **3. Reduction in Noise:** - Noise sources exist at the output and input of amplifiers. - Noise power in the amplifier with negative feedback is given by: - $N_f = \frac{N}{1+A\beta}$ - This indicates a reduction in the gain of the amplifier due to the negative feedback. - To maintain the original gain, we need to use additional stages. - This can potentially introduce more noise. - Negative feedback reduces the noise by a factor of 1+Aβ. - **5. Reduction in Distortion:** - Consider an amplifier with an open loop voltage gain (A_v) and a total distortion (D) without feedback. - Distortion with feedback is given by: - $D_f = \frac{D}{(1+A\beta)}$. - This implies that distortion is reduced by a factor of 1⁄(1+Aβ). - **4. Bandwidth (BW):** - Bandwidth is the difference between the upper and lower frequencies where the amplifier gain is more than 70.7 percent of the maximum. - Bandwidth without feedback: - $BW = f_h - f_l$ - Bandwidth with feedback: - $BW_f = f_{hf} - f_{lf}$. - Feedback increases the bandwidth. - $BW_f = BW (1+A\beta)$ - This means that the bandwidth of an amplifier with feedback is greater than the bandwidth of an amplifier without feedback. - **6. Effect of Negative Feedback of Input Resistance:** - When the negative feedback signal is fed back in series with the applied voltage, the input resistance will increase. - This is because the feedback voltage (Vf) opposes the source signal (Vs). - Input resistance with feedback is greater than the input resistance without feedback. - Input resistance with series feedback: - $R_{if} = R_i (1+A\beta)$ - When the negative feedback signal is fed back in shunt with the applied signal, the input resistance will decrease. - This is because the source current (Is) increases with feedback, while the input voltage (V_i) is smaller than the input voltage without feedback. - Input resistance with shunt feedback: - $R_{if} = \frac{R_i}{(1+A\beta)}$ - In other words, series mixing increases the input resistance, while shunt mixing decreases the input resistance. - **7. Effect of Negative Feedback on Output Resistance:** - Negative feedback decreases the output resistance. - When the load resistance (R_l) increases, the output voltage (V_o) also increases, but because of negative feedback, this increase is smaller than the increase without feedback. - This reduces the output resistance. - **Oscillators:** - When the input signal and part of the output signal are in phase, we have positive feedback. - Positive feedback leads to oscillations. - An oscillator is a circuit which produces periodic waveforms without an input signal. - **Applications of Oscillators:** - **Clock signals** - **Local oscillator** in a receiver to convert RF to IF signals. - **Sweep Circuits** in television sets and CROs. - **Generation of RF Carriers** in a transmitter. - **Barkhausen Criteria for Sustained Oscillations** - Conditions for sustained oscillations: - **1. Loop gain |Aβ| = 1** - **2. Total phase shift around the loop must be 0° (or) 360°**. - **Working of a Practical Oscillator:** - Loop gain(|Aβ| = 1) and phase shift (|Aβ| = 0° (or) 360°) conditions are necessary for sustained oscillations. - Initial thermal noise acts as an input signal. - Every resistance has some free electrons. - These electrons move randomly due to thermal energy, generating noise voltage. - This noise is amplified by the amplifier. - If the loop gain is greater than 1, the amplitudes of oscillations increase. - When the loop gain is equal to 1, the oscillations become sustained. - If the loop gain is less than 1, the amplitude decreases, and the oscillations damp out. - **Types of Oscillators:** - **LC Oscillator:** Uses inductor (L) and capacitor (C) in the tank circuit. - This circuit provides a phase shift of 180° through the tank circuit and another 180° from the amplifier. - The frequency of oscillation is given by: $f = \frac {1}{2 \pi \sqrt{LC}}$. - **LC Oscillator Configurations:** - **Hartley Oscillator:** Amplifier provides 180° Phase shift, and the tank circuit provides another 180°. - **Frequency of Oscillation:** - $f=\frac{1}{2 \pi \sqrt{(L_1+L_2+2M) C}}$ - **Condition for Sustained Oscillations:** - $hfe =\frac {L_1+M}{L_2+M}$. - **Colpitts Oscillator:** Amplifier provides 180° phase shift. The tank circuit provides 180° through a combination of two capacitors. - **Frequency of Oscillation:** - $f = \frac {1}{2 \pi \sqrt{LC_{eq}}}$. - **Condition for Sustained Oscillations:** - $hfe = \frac{C_2}{C_1}$. - **RC Phase Shift Oscillator:** Uses resistors (R) and capacitors (C) in the RC filter. - The amplifier provides 180° phase shift, and the RC phase shift network provides another 180° phase shift. - The frequency of oscillation is given by: $f = \frac{1}{2\pi RC \sqrt{6}}$. - **Wien Bridge Oscillator:** - Uses a wien bridge network, which acts as a lead-lag network. - The amplifier doesn't introduce any phase shift. - The frequency of oscillation is given by: $f=\frac{1}{2 \pi RC}$. - For sustained oscillations, the amplifier gain needs to be at least 3 (|A|≥3). - The bridge needs to be balanced, where: - $R_3=2R_4$. - The frequency of oscillation can be varied by changing the values of capacitors (C1 and C2). This structured information comes from the provided image. 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