Operational Transconductance Amplifiers (OTAs)
This chapter describes operational transconductance amplifiers (OTAs) and their linearization for use in g m -C filters. Super-source-follower and digitally programmable OTAs are detailed. The common-mode feedback used in these OTAs and a buffer amplifier
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Operational Transconductance Amplifiers (OTAs)
An ideal transconductance amplifier is a voltage-controlled current source, with an infinite input and output impedance. Beside in Gm -C filters, OTAs can be used in data converters, variable gain amplifiers and equalizers. In Fig. 4.1 the symbol of a single-ended and a fully-differential transconductor is shown. The factor between the output current and the input voltage is called transconductance. iout = Gm · (vinp − vinn )
(4.1)
One of the key attractive properties of OTAs is the fast speed in comparison to conventional operational amplifiers. The high-bandwidth capability of the OTA is in part due to the fact that the internal nodes are of low impedance. Usually, a transconductor consists of only one gain stage which means that no compensation capacitance is necessary. Non-ideal parameters of an OTA are the input capacitance Cin , the output capacitance Cout and the output conductance gout . These non-ideal parameters will limit the AC-performance of the OTA and of filters. The OTA frequency-dependent transconductance and input and output capacitances will affect mainly the high frequency characteristics. The finite output resistance will affect especially the low-frequency response of filters. The transconductance Gm is frequency dependent and can be described by a first-order low-pass Gm (j ω) =
Gm0 Gm0 = e−j Φ(ω) ω 2 1 + j ω/ωT 1 + ( ωT )
(4.2)
where Gm0 is the DC transconductance and ωT is the transit frequency of the OTA. When an OTA is applied to a Gm -C filter, ωT is usually much larger than the filter cut-off frequency fC . So the transconductance at fC can be described as Gm (j ωC ) ≈ Gm0 · e−j ΦE
(4.3)
where ΦE is the phase of the transconductance at the filter cut-off frequency and is called excess phase. H. Uhrmann et al., Analog Filters in Nanometer CMOS, Springer Series in Advanced Microelectronics 45, DOI 10.1007/978-3-642-38013-6_4, © Springer-Verlag Berlin Heidelberg 2014
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Operational Transconductance Amplifiers (OTAs)
Fig. 4.1 Symbol of a transconductor
Fig. 4.2 Simplest transconductor
For the design of high-frequency Gm -C filters the parasitic capacitances involve some problems. • The parasitic capacitances are usually not accurately known. For some highfrequency designs where the parasitics are a large part of the total integrating capacitance, this problem causes an increased uncertainty in the filter capacitance value. • In general, the parasitics are nonlinear. This induces distortion as well as the frequency response depends on the signal amplitude. • The presence of parasitics involves some mismatch between two integrators. For best matching, the fraction each type of parasitic contributes to the total integrating capacitance should be kept the same for all integrators. Another important issue is the input range that will give a constant transconductance. This is very important for determining the level of distortion of the output currents.
4.1 Linearization Techniques for OTAs The simplest transconductor consists
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