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Chapter 11: Problem 53

An amplifier has an input resistance of \(1 \Omega\) an output resistance of \(1 \Omega,\) and an open circuit voltage gain of 10 . Classify this amplifier as an approximate ideal type and find the corresponding gain parameter. In deciding on an amplifier classification, assume that the source and load impedance are on the order of \(1 \mathrm{k} \Omega.\)

Short Answer

Expert verified
The amplifier approximates an ideal voltage amplifier with a gain of 20 dB.

Step by step solution

01

Understand the Problem

The problem involves classifying an amplifier type based on its given properties and finding a corresponding gain parameter. The amplifier has given resistances and voltage gain; we are to assume typical source and load impedances to determine the type of amplifier it approximates.
02

Identify Approximate Ideal Amplifier Types

In electronics, ideal amplifier types include voltage amplifiers, current amplifiers, transconductance (V-to-I) amplifiers, and transresistance (I-to-V) amplifiers. Each has specific characteristics, such as very high or very low input/output resistances. We need to match these characteristics with the given parameters of the amplifier.
03

Analyze Input and Output Resistances

Given that both the input and output resistances are low (1 惟), and compared to the assumed source and load resistances (1 k惟), these are negligible. Typically for a voltage amplifier, the input should be high, but the dominance of the open-circuit voltage gain suggests it models a voltage amplifier more than others.
04

Determine the Approximate Type

With an open-circuit voltage gain of 10 and low input/output resistances, the amplifier mostly resembles an ideal voltage amplifier. For an ideal voltage amplifier, we assume a very high input resistance and a low output resistance.
05

Calculate Gain Parameter

The voltage gain, expressed in magnitude, is already given as 10. To express this in decibels (dB), use the formula: \[ G_{dB} = 20 \log_{10}(A_v) \] where \(A_v\) is the voltage gain. Substitute \(A_v = 10\).
06

Perform Calculation

Calculate the decibel gain using the formula: \[ G_{dB} = 20 \log_{10}(10) = 20 \, \text{dB} \]So, the gain in decibels is 20 dB.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Voltage Gain
Voltage gain is a crucial parameter in the world of amplifiers. It tells us how much an amplifier can increase the strength of a signal. Mathematically, voltage gain is defined as the ratio of output voltage to input voltage. In our exercise, this amplifier has a linear voltage gain of 10.
  • If the input signal has a voltage of 1 Volt, the output voltage will be 10 Volts.
  • This gain can also be expressed in decibels (dB), using the formula \[ G_{dB} = 20 \log_{10}(A_v) \] where \(A_v\) is the voltage gain.
  • In the exercise, substituting \(A_v = 10\) into the formula gives us a gain of 20 dB.
Choosing to express gain in decibels is common because it simplifies calculations, especially when dealing with different stages in audio equipment or telecommunication systems.
Input and Output Resistance
The input and output resistance of an amplifier define how it interacts with other electrical components.
  • Input Resistance: Ideally, it should be very high for voltage amplifiers, minimizing the current drawn from the source. Some amplifiers have a resistance of up to mega-ohms.

  • Output Resistance: Ideally, it should be very low to ensure efficient power delivery to the load.
In the given problem, both the input and output resistances are 1 惟. These are relatively low compared to the assumed source and load impedances of 1 k惟 in our exercise.
  • These resistance values suggest that neither input nor output resistance dominates the amplifier's characteristics, making it more reflective of an ideal voltage amplifier.
  • The low output resistance ensures that the maximum voltage is transferred to the load, aligning with our existing characteristics.
Ideal Amplifier Types
Understanding ideal amplifier types helps in categorizing and using them effectively. Generally, amplifiers fall into four broad classifications:
  • Voltage Amplifiers: High input resistance, low output resistance. Designed to boost the voltage of a signal.

  • Current Amplifiers: Low input resistance and high output resistance, intended to increase the current capability of an input signal.

  • Transconductance Amplifiers (V-to-I): Converts input voltage into output current.

  • Transresistance Amplifiers (I-to-V): Converts input current into output voltage.
The problem points towards a voltage amplifier due to its voltage gain and low output resistance characteristics.
  • Despite having low input resistance, the overall architecture leans more towards the traits of a voltage amplifier.
Recognizing the subtle traits of each amplifier type is crucial for designing circuits that meet specific performance criteria.

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Most popular questions from this chapter

An amplifier is needed as a part of a system for documentation of voltages in the earth created by an electrical power distribution system, Voltage waveform occurring between probes to be placed in the earth are to be amplified before being applied to the analog-to-digital converter (ADC) inputs of laptop computers. The internal impedance of the probe can be as high as \(10 \mathrm{k} \Omega\) in dry sand or as low as \(10 \Omega\) in muck. Because several different models of ADCs are to be used in the project, the load impedance for the amplifier varies from \(10 \mathrm{k} \Omega\) to \(1 \mathrm{M} \Omega\) Nominally, the voltage applied to the ADC is required to be 1000 times the open-circuit voltage of the probe 卤3 percent. What type of ideal amplifier is best suited for this application? Using your best judgment, find the specifications for the impedance and gain parameter of this amplifier.

The output terminals of an ideal voltage amplifier are connected to the input terminals of an ideal trans conductance amplifier. What type of ideal amplifier results? Deter mine its gain parameter in terms of the gain parameters of the separate stages.

The transfer characteristic of an amplifier is described by the equation $$v_{o}(t)=10 v_{\mathrm{in}}(t)+0.6 v_{\mathrm{in}}^{2}(t)+0.4 v_{\mathrm{in}}^{3}(t)$$ For the input \(v_{\mathrm{in}}(t)=2 \cos (200 \pi t),\) determine the distortion factors \(D_{2}, D_{3},\) and \(D_{4}\) Also, compute the total harmonic distortion. You may find the following trigonometric identities useful: $$\begin{array}{l} \cos ^{2}(A)=\frac{1}{2}+\frac{1}{2} \cos (2 A) \\ \cos ^{3}(A)=\frac{3}{4} \cos (A)+\frac{1}{4} \cos (3 A) \end{array}$$

In your own words, describe a situation in which a small differential signal is of inter est and a large common-mode signal is also present.

Describe an application in which an amplifier with very high input impedance is needed.
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