## Electronics Reference

# Operational Amplifiers (Basic Circuits)

Common-Mode Rejection Ratio | A_{ol} - Open-Loop Differential Voltage GainA _{cm} - Common-Mode Gain |

Input Bias Current | |

Input Offset Current | |

Offset Voltage | |

Error Output Voltage | |

Slew Rate |

**Common-Mode Rejection Ratio** (**CMRR)**

In an op-amp, the desired input signal can only occur on one input. Signals may occur on the two inputs, however they must have different polarities. The purpose of this is that if unwanted signals such as noise occur on both input lines with the same polarity, they are cancelled by the op-amp so that they won’t be amplified and don’t appear on the output. The measure of an op-amp’s ability to reject common-mode signals is called common-mode rejection ratio (CMRR). A_{ol} is the open-loop differential voltage gain and A_{cm} is the common-mode gain of the op-amp.

Input Bias Current (I_{BIAS})

Ideally, there should be no current flowing through the op-amp’s inputs. However, in reality there is this input bias current that is required by the inputs of the op-amp to bias the first stage of the op-amp. Input bias current is the average of the two input currents, I_{1} and I_{2}.**Input Offset Current (I**_{OS}**)**

Ideally, input bias currents should be equal but in reality, they are not. The difference between the two input bias currents, which is an absolute value, is called input offset current.

Offset Voltage (V_{OS})

The product of the input offset current and the input impedance of the op-amp.

Error Output Voltage, V_{OUT(ERROR)}** _{}**Amplified offset voltage by the op-amp’s gain.

Slew Rate

Slew Rate

The maximum rate of change of the op-amp’s output in response to a step input voltage.

Feedback Circuit Attenuation | |

Voltage Gain | |

Input Impedance | Z_{in} - Open-loop input impedance of the op-amp |

Output Impedance | Z_{out} - Open-loop internal output impedance of the op-amp |

_{}Feedback Circuit Attenuation (B)

The attenuation (B) caused by the feedback circuit composed of R_{f} and R_{i}.

Voltage Gain, A_{cl(NI)}

The closed-loop gain of noninverting amplifier configuration which is reciprocal of the attenuation of the feedback circuit.**Input Impedance, Z**_{in(NI)}

Closed-loop input impedance of noninverting amplifier configuration where A_{ol} is the open-loop gain of the op-amp, B is the attenuation, and Z_{in} is the open-loop input impedance of the op-amp.**Output Impedance, Z**_{out(NI)}_{}_{}

Output impedance of noninverting amplifier configuration with negative feedback where Z_{out} is the open-loop internal output impedance of the op-amp.

Voltage Gain | |

Input Impedance | Z_{in} - Open-loop input impedance of the op-amp |

Output Impedance | Z_{out} - Open-loop internal output impedance of the op-amp |

**Voltage Gain, A _{cl(VF)}**

Voltage follower configuration is just like a noninverting amplifier configuration with its output fed back to its inverting input by a straight connection making its attenuation equal to 1. Since the gain of a noninverting amplifier configuration is just the reverse of its attenuation, the voltage gain of a voltage follower is also 1, which means there is no gain.

**Input Impedance, Z**

_{in(VF)}The same input impedance formula of noninverting amplifier configuration but with B equal to 1 and greater input impedance.

**Output Impedance, Z**

_{out(VF)}The same output impedance formula of noninverting amplifier configuration but with B equal to 1 and much smaller output impedance.

Feedback Circuit Attenuation | |

Voltage Gain | |

Input Impedance | |

Output Impedance | Z_{out} - Open-loop internal output impedance of the op-amp |

_{}Feedback Circuit Attenuation (B)

The attenuation (B) caused by the feedback circuit composed of R_{f} and R_{i}.

Voltage Gain, A_{cl(I)}

Closed-loop voltage gain of inverting amplifier configuration which is the ratio of R_{f} to R_{i}.**Input Impedance, Z**_{in(I)}

Inverting amplifier input impedance is equal to R_{i} because the inverting input is at virtual ground and the input source sees R_{i} to ground.**Output Impedance, Z**_{out(I)}

The same output impedance formula of noninverting amplifier configuration._{}

**Open-Loop:**

Bandwidth (BW)In general, bandwidth is the difference between the upper critical frequency (f _{cu}) and lower critical frequency (f_{cl}) of an amplifier. Since the f_{cl} of an op-amp is zero, its bandwidth is equal to its f_{cu}. | |

Internal RC lag circuit attenuationOp-amps internal RC lag circuit attenuation. The RC lag circuits inside an op-amp causes roll-off in gain as frequency increases. | |

Open-Loop Gain (A_{ol})The open-loop gain of an op-amp is the product of the midrange open-loop gain (Aol(mid)) and the internal RC lag circuit attenuation. | |

Phase Shift (θ)A phase shift created between the input signal and the output signal because of the delay caused by the internal RC lag circuit. |

**Closed-Loop:**

Critical Frequency, f_{c(cl)}The closed-loop critical frequency of an op-amp. The negative feedback extends the critical frequency of an op-amp. _{} | |

Bandwidth (BW_{cl})The closed-loop bandwidth of an op-amp. As the negative feedback increases the limit of an op-amp’s critical frequency, it also extends the bandwidth of the op-amp. | |

Unity-gain BandwidthBandwidth which is equal to the frequency at which the open-loop gain of an op-amp is unity or 0dB. |

Upper Trigger Point Voltage | |

Lower Trigger Point Voltage | |

Hysteresis Amount |

**Upper Trigger Point Voltage (V _{UTP})**

To make a comparator insusceptible to noise, a technique that uses positive feedback called hysteresis can be used. The upper trigger point voltage is a reference level wherein the output switches to maximum negative voltage from the maximum positive voltage when the input exceeds the upper trigger point.

Lower Trigger Point Voltage (V

Lower Trigger Point Voltage (V

_{LTP})The lower trigger point voltage is a reference level wherein the output switches to maximum positive voltage from the maximum negative voltage when the input goes below the lower trigger point.

Hysteresis Amount (V

Hysteresis Amount (V

_{HYS})The hysteresis amount is determined by the difference between the V

_{UTP}and the V

_{LTP}.

A summing amplifier is an op-amp configuration that can add or mix two or more input signals. Basically, it’s like an inverting amplifier with more input signals and resistors. Its output voltage is proportional to the negative of the algebraic sum of its input voltages.

An integrator is an op-amp configuration that simulates mathematical integration. Its output voltage is proportional to the input voltage integrated over time.

A differentiator is an op-amp configuration that simulates mathematical differentiation. It produces an output that is proportional to the rate of change of the input voltage.