Logarithmic Variable Gain Amplifier and Filter Control
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Solution Overview
Problem
Existing analog filters and amplifiers face inefficiencies and inaccuracies in logarithmically controlling variable gain and cutoff frequency due to non-linearity in digital resistance changes, leading to uncontrollable sections and quantization errors, especially in high frequency bands, requiring complex digital logic circuits for accurate dB and log scale conversions.
Innovation Solution
A variable resistance circuit with operational amplifiers and digital control codes that linearly change resistance on a dB basis for gain and inversely on a log scale for cutoff frequency, using a logic circuit for AND and NOT operations to determine resistances, allowing direct digital control of gain and cutoff frequency without complex digital logic, and minimizing quantization errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a binary structure variable resistor with linear resistance change according to digital code is used, then the circuit complexity is reduced, but the control precision and accuracy in high frequency bands deteriorates due to non-linearity in log domain
Solution Approach 1:
The patent changes the resistance values of the variable resistors from a linear binary structure (2R, 4R, 8R, 16R, ..., 2^nR) to a logarithmic structure where resistance values are proportional to 2^(k/2^m) * R. This parameter change ensures that when the digital code K varies linearly, the resistance changes logarithmically, which matches the log scale representation of the frequency axis and dB gain units, thereby improving control precision without increasing circuit complexity
Solution Approach 2:
The patent makes the resistance values dynamically adjustable according to the digital code K, where each increment of K produces a consistent logarithmic change in resistance. This dynamic adjustment mechanism ensures uniform control characteristics across the entire frequency range, eliminating the uncontrollable sections that occur in high frequency bands with linear resistance structures
2Measurement precision
If the digital code K is increased to reduce quantization error, then the measurement precision improves, but the device complexity increases due to additional bits and logic circuits
Solution Approach 1:
The patent changes the resistance scaling factor from linear (2R, 4R, 8R, ...) to logarithmic (2^(k/2^m) * R), which fundamentally alters how quantization error behaves. With this change, the quantization error becomes uniform across the entire frequency range rather than increasing in high frequency bands. This allows achieving consistent precision with fewer bits, reducing device complexity while maintaining measurement precision
3Ease of operation
If linear resistance change is used for simplicity, then the ease of operation is improved, but the reliability deteriorates due to uncontrollable sections in high frequency bands
Solution Approach 1:
The patent changes the resistance values to follow a logarithmic progression (proportional to 2^(k/2^m) * R) instead of linear progression. This parameter change ensures that the relationship between digital code K and resistance remains consistent across all frequency bands, eliminating uncontrollable sections in high frequency bands and improving reliability while maintaining ease of operation through simple digital control
Data Source
AI summary
A variable gain amplifier circuit is provided. The circuit includes an operational amplifier for amplifying and outputting an input signal according to a cutoff frequency and a gain, a feedback resistor for changing a first resistance according to a first digital control code value which determines the cutoff frequency, and an input resistor for changing a second resistance according to a second digital control code value which is determined based on a difference of the first digital control code value and a gain code value. The gain is determined by a ratio of the first resistance and the second resistance and linearly changes on a decibel (dB) basis according to the first digital control code value, the cutoff frequency is inversely proportional to the first resistance and linearly changes on a log scale, and the variable gain can be easily set using the control code.