The present invention relates generally to signal amplifiers, and in particular to signal amplifiers having a non-linear transfer function. The amplifiers of the present invention have a wide range of applicability, including, for example, in mass spectrometry devices or cameras.
In many signal processing applications, it is often desirable to digitize analog signals. For example, it is often desirable to convert analog signals representing detected physical events or phenomenon to digital signals for further processing in a digital computer system. To do so, analog signals are typically sampled at a certain rate and converted to digital bits using a digitizer, e.g., an analog-to-digital converter (ADC).
An ideal digitization system that is able to handle high dynamic range and high bandwidth signals is difficult to realize. Dynamic range refers to the ratio between the maximum signal level and the minimum signal level that can be handled by the electronic system. Often, the maximum level corresponds to the largest signal that can be handled without clipping or other substantial distortion, and the minimum signal level is determined by the larger of the noise level for small signals or the resolution of the digitizer for small signals. In electrical transmission systems, bandwidth refers to the range between the highest and lowest frequencies of a transmission channel. Bandwidth is typically measured in Hertz (Hz, cycles per second). For a signal sampled at discrete time intervals, the bandwidth of the signal is limited to one half the sampling rate (the Nyquist frequency).
A mass spectrometer is a good example of a system that requires a digitization system that can handle transient signals from the mass spectrometer that have a high dynamic range and large bandwidth. Ideally the dynamic range of a mass spectrometer designed for protein profiling will match the dynamic range of the concentration of proteins present in blood serum, or about 1015. This dynamic range is many orders of magnitude beyond the capability of any currently available protein profiling system including those using mass spectrometry. The realizable dynamic range of protein profiling systems using mass spectrometry techniques is currently closer to 105. Part of this dynamic range can be practically realized using signal averaging, but much of it must be accounted for directly with the digitization system.
In a time-of-flight mass spectrometer (TOF-MS) system, the time resolution of the digitization system is one of the factors that determines the mass resolution that can be realized by the system. Ideally the time resolution of the mass spectrometer is limited by the detection system or the performance of the mass analyzer rather than the digitization system. Currently available ion detectors produce output signals with pulse widths ranging from tenths of nanoseconds to a few nanoseconds. Effectively digitizing these signals without loss of time resolution requires digitization systems with bandwidths from about 100 to about 5000 MHz.
Consider a digitization system with a dynamic range of approximately 7000 and a bandwidth of approximately 320 MHz. Using standard techniques such a system would require a 13-bit linear analog-to-digital converter (ADC) with a bandwidth greater than 320 MHz. Currently it is difficult and expensive to produce systems with such high combined dynamic range and bandwidth. However, the situation can be improved by considering the noise characteristics of the signal being processed. In general, all analog signals have noise.
A typical ADC is a substantially linear device that simply outputs a number proportional to the input at a fixed sampling rate. The dynamic range is usually determined by the largest number that the ADC can output. This dynamic range is usually 2n where n is this number of digital bits used to represent the output number. Implicit in this calculation of the dynamic range is the assumption that the smallest signal that can be effectively measured is represented by a change of 1 in the output of the ADC. Thus, for a particular ADC there is a trade off between the largest signal measured and the amplitude resolution achieved. Choice of useful amplitude resolution is generally limited by noise; very little is gained by digitizing a signal with an amplitude resolution finer than the amplitude of the noise on the signal.
In general, the noise characteristic of a signal can vary with the amplitude of the signal. Further, the noise characteristic of a signal typically contains contributions from many different sources. In many electronic systems, for example, the amplitude of the noise is essentially independent of the amplitude of the signal (i.e., constant). This is usually true where the main noise contribution is, for example, thermal noise in amplifiers and other circuit components. Another type of noise, shot noise, arises when a signal is composed of discrete elements. For example, any electronic signal associated with a current has shot noise because the current is made up of discrete charge carriers, usually electrons. The amplitude of shot noise is proportional to the square root of the amplitude of the signal. Since most electronic signals involve extremely large numbers of electrons, the shot noise is often a very small fraction of the amplitude of these signals and is often a negligible portion of the total noise in the system. Shot noise also occurs when the signal is due to the detection of particles such as photons or charged or neutral particles. Thus, in a system such as a mass spectrometer, where the numbers of ions detected can be as low as a few or even single ions, shot noise can dominate all other noise sources.
The noise characteristic of the signal and the resolution of the digitization system can be matched by choosing the resolution of the digitizer to be roughly equivalent to the noise amplitude (Note that the peak-to-peak noise amplitude will usually be a few times the noise amplitude measured, for example, with a standard deviation). In this way, the largest possible signal is accommodated while the resolution of the system is limited by the noise in the signal and not by the resolution of the digitization (noise limited resolution). This is straight forward for a signal where the noise amplitude is constant. For a linear ADC, this procedure optimizes the dynamic range of the measurement system by minimizing the digitization levels devoted to measuring the noise in the signal and allowing the signal amplitude to be as large as possible. However, for a signal where the noise amplitude changes with signal amplitude, the situation is not so simple. With a linear ADC, matching the resolution to the amplitude of the noise at one signal amplitude will either cause the digitizer to become the resolution limiting factor at signal amplitudes where the noise is smaller or digitizer resolution will be wasted at signal amplitudes where the noise is larger.
This situation can be improved by constructing a digitization system where the resolution changes with signal amplitude such that the resolution is always matched to the amplitude of the noise. One way of doing this is to transform the signal before it is digitized with a linear ADC such that the noise amplitude of the transformed signal is a constant, i.e., the noise amplitude does not vary with the amplitude of the signal. For example, for a signal where the noise amplitude characteristic is dominated by shot noise (noise amplitude increases with the square root of the signal amplitude), the required transformation is to take the square root of the signal before digitizing with a linear ADC. Linear and logarithmic transformations are not optimal when the noise characteristic of the signal is dominated by shot noise. For example, with a linear transformation of the input signal before digitization with a linear ADC, the noise amplitude of the transformed signal will increase with larger signal amplitude exactly as it did in the untransformed signal. If the resolution is matched to the noise amplitude at low signal levels where the noise amplitude is smallest, then resolution will be wasted on high amplitude signals where the noise amplitude is larger. With a logarithmic transformation of the input signal before digitization with a linear ADC, the noise amplitude of the transformed signal will decrease with larger signal amplitude. If the resolution is matched to the noise amplitude at high signal levels where the noise amplitude is smallest, then resolution will be wasted on low amplitude signals where the noise amplitude is larger.
However, it is difficult to design amplifiers with particular non-linear transforms, such as a square root transform, and particularly difficult to design such amplifiers to handle high bandwidth signals, for example, signals with bandwidths greater than 100 MHz.
It is therefore desirable to provide an amplifier circuit that provides a non-linear transfer function, and particularly a square root transfer function. Such an amplifier circuit should also operate with a high dynamic range and a large bandwidth. It is also desirable to use such an amplifier in a mass spectrometer device or in a camera.