Institute of Industrial Electronics Engineering

Third-Year

Integrated Circuits(IE-303)

Assignment

Log and Antilog Amplifiers

Dated: Roll No.:21-07-10 1936

Log and Antilog Amplifiers

Background:

A logarithmic scale is a scale of measurement that uses the logarithm of a physical quantity instead of the quantity itself. It is used in conjunction with units such as with Bel which a logarithmic unit of measurement that expresses the magnitude of a physical quantity (power or intensity) relative to a specified or implied reference level.

B = log (Power Ratio)

Since it expresses a ratio of two quantities with the same unit, it is a dimensionless unit. The Bel unit is quite large, instead we use decibel (dB) which is one-tenth of a Bel.

dB = 10 log (Power Ratio)

One may ask, if one dB is one tenth of a Bel, should the scaling factor in above equation be 0.1 instead of 10? That is not correct though, because to achieve a finer unit step we need to have a power ratio of 10:1 show as ten steps. Thus we get the above equation.

Why do we use Logarithmic Scale? The decibel's logarithmic nature means that a very large range of ratios

can be represented by a convenient number, in a similar manner to scientific notation. This allows one to clearly visualize huge changes of some quantity.

The mathematical properties of logarithms mean that the overall decibel gain of a multi-component system (such as cascaded amplifiers) can be calculated simply by summing the decibel gains of the individual components, rather than needing to multiply amplification factors.

Operational Amplifiers for Log-Antilog Functions:

1.1.Fundamentals of Log Amplifiers:

1.2. Basic Logarithmic Amplifier:

1.3. Basic Log Amplifier Using Diode:

1.4. Basic Log Amplifier Using Transistor:

1.5. Disadvantages of Basic Circuit:

1.6. Temperature Compensated Log Amplifier:

1.7. Frequency Compensation for Log Amplifier:

2. Antilog Amplifier:

2.1. Basic Antilog Amplifier Using Diode:

2.2. Basic Antilog Amplifier Using Transistor:

2.3 Temperature Compensated Antilog Amplifier:

Why the Use of Transistor is Preferred Over Diode in Log-Antilog Amplifiers?

Both log amplifiers and antilog amplifiers are practically obtained by using transistors as compared to diodes because the transistors give high accuracy, reduced bulk resistance and high range of operations.

A practical problem with a simple diode is the inherent internal resistance of any semiconductor material. This resistance is also subject to change with temperature, and may actually cause some internal heating in some applications.

Operation of diode log converters is not practical over two decades for true log characteristics. For the case of transistors, their reverse saturation current of the emitter-base junction (IS) < 10-14 A, which is orders of magnitude better than the reverse saturation current (I0) of diodes. Thus an expanded range of logarithmic operation (6 to 8 decades) can be achieved by using a transistor.