Inverting amplifier configuration

1. Inverting amplifier configuration:

• An inverting amplifier configuration is a type of operational amplifier (op-amp) circuit that produces an output signal that is inverted (i.e., phase-shifted by 180°) and amplified version of the input signal.
• Characteristics:
• – Input signal is applied to the inverting input terminal (marked with a minus sign)
• – Output signal is inverted and amplified version of the input signal
• – Gain is negative (i.e., output signal is opposite in polarity to the input signal)
• – Feedback resistor (Rf) is connected between the output terminal and the inverting input terminal.
• 
• Figure 1 Inverting amplifier
• Using virtual earth analysis, and the assumptions noted below, we can derive the transfer function (voltage output equation) for this type of circuit.
• Formula:
• [math]Gain (Av) = – \frac{R_f}{R_{in}}[/math]
• Where [math]R_{in} [/math] is the input resistance and [math]R_f [/math] is the feedback resistance.
• Advantages:
• – Inverting amplifier provides a high gain without sacrificing bandwidth
• – Can be used for both AC and DC coupling
• – Provides a phase shift of 180° between input and output signals
• Assumptions:
• – Ideal voltage gain: The op-amp has an infinite voltage gain ([math]A_v = ∞ [/math]).
• – Infinite input impedance: The input impedance of the op-amp is infinite ([math]Z_{in} = ∞ [/math]), meaning it doesn’t draw any current from the input source.
• – Zero output impedance: The output impedance of the op-amp is zero ([math]Z_{out} = 0 [/math]), meaning it can drive any load without affecting the output voltage.
• – No offset voltage: The op-amp has no offset voltage ([math]V_{OS} = 0 [/math]), meaning the output voltage is exactly zero when the input voltage is zero.
• – Infinite bandwidth: The op-amp has an infinite bandwidth ([math]BW = ∞), meaning it can amplify signals of any frequency without attenuation.
• – No noise: The op-amp generates no noise ([math] V_n = 0 [/math]), meaning the output signal is perfectly clean and free of any noise or distortion.
• – Linear operation: The op-amp operates in a linear region, meaning the output voltage is directly proportional to the input voltage.
• – No saturation: The op-amp does not saturate ([math] V_{out} = ∞ [/math]), meaning the output voltage can swing to any value without clipping or distortion.
• These assumptions are idealizations, and real op-amps may deviate from these assumptions. However, they provide a useful framework for analyzing and designing op-amp circuits.
• By looking at the inverting amplifier configuration, the non-inverting input voltage is 0V (as it is connected to the ground). And as the op-amp is ideal, it has infinite open-loop gain ([math]A_{OL} [/math]). Using these pieces of information, can rewrite the open-loop transfer function as
• [math]\begin{aligned}
  V_{\text{out}} &= A_{\text{OL}}  (V_+ – V_-) \\
  V_{\text{out}} &= \infty \times (0 – V_-) \\
  V_- &= -\frac{V_{\text{out}}}{\infty} \\
  V_- &= 0 \, \text{V}
  \end{aligned}[/math]
• Because it is split by the infinite open-loop gain, the voltage at the inverting input is so minimal that it may be considered zero, as this equation demonstrates. Because it (virtually) has a value of 0 V while not being linked to the earth, this point in the circuit is called a virtual earth. A red cross indicates the virtual earth’s placement on the circuit on the right.
• 
• Figure 2 Graph between lower levels of distortion

2. Derivation of [math]\frac{V_{\text{out}}}{V_{\text{in}}} = -\frac{R_f}{R_{\text{in}}}[/math]

• The derivation of the formula [math]\frac{V_{\text{out}}}{V_{\text{in}}} = -\frac{R_f}{R_{\text{in}}} [/math]for an inverting amplifier is as follows:
• Assume an ideal op-amp with infinite gain ([math]A_v= ∞ [/math]) and infinite input impedance ([math]Z_{in} = ∞[/math]).
• 
• Figure 3 Using Op-Amp for calculation
• As the op-amp is ideal, its input resistance is infinite so no current will be drawn into the inverting input, meaning [math]I_X = 0A [/math].
• Using Kirchoff’s current law, which states that the total current flowing into a junction is equal to the current flowing out of that junction, we can see that current passing through [math]R_{in} (I_{R1}) [/math] is equal to the current passing through [math]R_f (I_{Rf})[/math], so [math]I_{R1} = I_{Rf}[/math].
• Using ohm’s law, the voltage across [math]R_{in} (I_{R1}) \text{ and } R_f (I_{Rf})[/math]:
• [math]V_{R1} =I_{R1} × R_1 \qquad V_{Rf} = I_{Rf} × R_f [/math]
• As [math] I_{R1} = I_{Rf} [/math] rearrange the equations for current, then rearrange the final equation for [math] V_{RF} [/math]
• [math] \begin{gather}
  I_{R_1} = \frac{V_{R_1}}{R_1}, \qquad I_{R_f} = \frac{V_{R_f}}{R_f} \\
  \frac{V_{R_1}}{R_1} = \frac{V_{R_f}}{R_f} \\
  V_{R_f} = \frac{V_{R_1}}{R_1} \times R_f
  \end{gather} [/math]
• Using kirchoff’s voltage law, which states that the sum of all the voltages in closed loop is equal to zero, we can find the value of [math]V_{out}[/math]. The only two voltages involved in the loop containing the op-amp and the output are [math] V_{Rf}  \text{ and } V_{out} [/math]  so……
• [math]V_{R_f} + V_{\text{out}} = 0 \\  V_{\text{out}} = -V_{R_f} [/math]
• Using the equations defined in the last two steps, we can form the transfer function.
• [math]V_{\text{out}} = -\left(\frac{V_{R_1}}{R_1} \cdot R_f\right) \\ \frac{V_{\text{out}}}{V_{R_1}} = -\frac{R_f}{R_1} [/math]
• [math]V_{R1}[/math] can be rewritten as [math]V_{in} \text{ and } R_1 [/math] can be rewritten as  to get the following equation:
• [math]\frac{V_{\text{out}}}{V_{\text{in}}} = -\frac{R_f}{R_{\text{in}}} [/math]

Non-inverting amplifier configuration:

3. Non-inverting amplifier configuration:

• In a non-inverting amplifier configuration, the input signal is applied to the non-inverting input terminal (marked with a plus sign) of the operational amplifier (op-amp). The output signal is in phase with the input signal, meaning that the output voltage swing is in the same direction as the input voltage swing.
• 
• Figure 4 non-inverting amplifier
• Characteristics:
• – Input signal is applied to the non-inverting input terminal (plus sign)
• – Output signal is in phase with the input signal
• – Gain is positive (output signal has the same polarity as the input signal)
• – Feedback resistor ([math]R_f = R_2[/math]) is connected between the output terminal and the inverting input terminal (minus sign)
• Formula:
• [math]\text{Gain (A}v\text{)} = 1 + \frac{R_2}{R_1} \\
  \text{Gain (A}v\text{)} = 1 + \frac{R_f}{R_{in}} [/math]
• Where [math]R_{in} = R_1[/math] is the input resistance and [math]R_f [/math] is the feedback resistance.
• It is important to note that the gain can never be lower than 1.
• An advantage of this circuit over the inverting amplifier circuit is that the input signal is connected directly to the op-amp, meaning the entire circuit draws no current due to the op-amp’s infinite input resistance.
• Whereas the inverting amplifier circuit will draw a current across [math]R_f [/math]. If the resistance of [math]R_f [/math] becomes 0 and/or the resistance of [math]R_{in}[/math] becomes infinite the following circuit is formed:
• Advantages:
• – Non-inverting amplifier provides a high gain without inverting the input signal
• – Has a high input impedance and a low output impedance
• – Can be used for both AC and DC coupling
• Applications:
• – Non-inverting amplifier is commonly used in:
  • – Audio amplifiers
  • – Instrumentation amplifiers
  • – Active filters
  • – Differential amplifiers
• The non-inverting amplifier configuration is another commonly used op-amp configuration, and it’s widely used in many electronic circuits.
• If the resistance of [math]R_f[/math] becomes 0 and/or the resistance of [math]R_1[/math] becomes infinite the following circuit is formed:
• 
• Figure 5 Non-inverting operational amplifier with resistances
• Since the op-amp has a gain of 1, no amplification takes place, so the circuit above is referred to as a unity gain buffer (or unity gain amplifier).
• These circuits are utilized as an interface between a low input resistance device that draws little or no current and a signal source.
• The original circuit won’t be disturbed because this buffer will take very little current while still producing the same input signal due to the op-amp’s infinite input resistance.

summing amplifier configuration

4. Summing amplifier configuration:

• A summing amplifier is a type of operational amplifier (op-amp) configuration that sums multiple input signals and produces an output signal that is proportional to the sum of the input signals.
• Characteristics:
• – Multiple input signals are applied to the inverting input terminal (marked with a minus sign)
• – Each input signal is multiplied by a corresponding weight or gain
• – The output signal is the sum of the weighted input signals
• – Feedback resistor ([math]R_f[/math]) is connected between the output terminal and the inverting input terminal (minus sign)
• – Multiple signals can be linked to an inverting amplifier and amplified separately thanks to a summing amplifier design.
• – An inverting amplifier’s virtual earth enables interference-free signal connection. An example of a summing amplifier arrangement is shown below.
• 
• Figure 6 Op-Amp with multiple resistance attach with inverting Op-amp
• The transfer function of a summing amplifier configuration is given below:
• [math]V_{\text{out}} = -R_f \left( \frac{V_1}{R_1} + \frac{V_2}{R_2} + \frac{V_3}{R_3} + \cdots \right) [/math]
• This type of amplifier is most commonly used as an audio mixer, where different audio inputs can be merged and their individual levels adjusted.

5. Difference amplifier configuration:

• A difference amplifier, also known as a differential amplifier, is a type of operational amplifier (op-amp) configuration that amplifies the difference between two input signals.
• Characteristics:
• – Two input signals, [math]V_1 \text{ and } V_2[/math], are applied to the inverting and non-inverting input terminals, respectively
• – Output signal is proportional to the difference between the two input signals ([math]V_1 – V_2 [/math])
• – Feedback resistor ([math]R_f[/math]) is connected between the output terminal and the inverting input terminal (minus sign)
• – Gain is set by the ratio of resistors ([math]\frac{R_f}{R_1} \text{ and }\frac{R_f}{R_2}[/math])
• Formula:
• [math]V_{\text{out}} = (V_+ + V_-) \frac{R_f}{R_1}[/math]
  
• This type of amplifier is often used in noise cancellation, below are two examples:
• 1. Balanced Microphone Amplifier:
• A balanced microphone amplifier is a type of amplifier used to amplify the signal from a balanced microphone. It’s designed to reject noise and hum, and provide a high-quality audio signal.
• Characteristics:
• – Differential input stage
• – High common-mode rejection ratio (CMRR)
• – Low noise and distortion
• Typically used in professional audio applications
• 2. ECG (Electrocardiogram) Amplifier:
• An ECG amplifier is a specialized amplifier used to amplify the tiny electrical signals generated by the heart, as measured by electrocardiography (ECG) electrodes.
• Characteristics:
• – High gain and high sensitivity
• – Low noise and distortion
• – Bandwidth limited to the frequency range of interest (typically 0.05-150 Hz)
• – High input impedance to minimize electrode offset voltage
• – Often includes filtering and signal processing to enhance signal quality
• Both of these amplifiers are designed for specific applications and have unique characteristics that enable them to effectively amplify and condition the signals they’re intended to work with