log domain filter

😎hi ! I m an electronics & comm. engineer. i have selected a second order log domain band pass filter for audio frequency applications as a project title. Log-domain filters comprise a subclass of circuits having externally linear transfer functions but internally nonlinear components . As the name implies, log-domain filters are specifically those circuits whose internal state is a logarithmic function of the input and output. An important property of log-domain filters is that the equations governing the internal nonlinearity of the system are generally tractable, leading to complete solutions which do not require separate DC and transient analyses.
Log-domain filters, which represent the most promising form of instantaneous companding filters, need an exponential nonlinearity for their realization. The exponential nonlinearity of the bipolar junction transistor has been used successfully to implement log-domain fiters in Bipolar/BiCMOS technologies.
These type of filters are called ELIN (Externally Linear Internally Non-linear) type filters.

Log-domain filters have received considerable attention due to their potential advantages over conventional continuous-time filters.
In these filters, the input current signal is first mapped using a natural logarithmic function. The resulting logarithmic signal is then processed in the log-domain,and the output is recovered using an exponential function to generate a current which is a linearly filtered version of the input. Mapping of the input current with the natural logarithm amounts to forcing the current through a diode, producing a voltage which is applied to the actual log filter. The log filter output voltage is mapped to a linear output current with an exponential function by applying this voltage to the base of a n-p-n transistor whose emitter is grounded and collector sinks the desired linear output current.
The compression process can be performed by the log—in circuit while an exponential output circuit, known as log-out is required to obtain linear response.

Since the companding mapping is inverse, the overall response remains linear.

Advantages of log-domain circuits over conventional continuous time filter circuits are inherent linearity without the need for negative feedback or degeneration; superior noise performance, improved high-frequency response, and wider operating bandwidth due to the low impedances nodes along the signal path; low-voltage operation, since node-voltage swings are greatly reduced while currents, not limited by the supply voltage, can still have a large
dynamic range; transconductance amplifiers employed in log domain filters are realized through employment of only a few transistors whereas the transconductance amplifiers which are designed for linear V-I characteristics used for developing conventional filters employs excessive transistors, resulting in efficient possible circuit topology designs that have more bandwidth and consumes less power in relation to the conventional filters; and use of grounded capacitors which are ideal for contemporary IC design techniques.


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