Multistage amplifier problems with facebook

In a given linear, multistage, cascaded amplifier [ 1 ] comprising passive coupling circuits and active two-ports alternatively, the problem is where in the amplifier the stabilizing circuit elements should be placed to eliminate instability, and of what type and value. Our investigations are based on a new recursive formula for the determinant of tridiagonal matrices. Relation of our results to the Stern stability factor has been obtained. A verification in numerical examples has also been provided. Stability Theory is currently being revived in many disciplines. This is because of the novel results in chaotic systems and investigations into its robustness.

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• Fiber Amplifiers
• Electronic Design - From Concept to Reality
• Degree in Computer Engineering
• Electronic devices
• ECE 320 - Linear Active Circuit Design (3)
• If All Else Fails, Read This Article. Avoid Common Problems When Designing Amplifier Circuits
• Final Exam - Fall 2009 Time allowed:-3 hrs Electronics I January 21 ...

WATCH RELATED VIDEO: Solved Problem on Multistage Amplifier, LIC

Fiber Amplifiers

Photodiodes - From Fundamentals to Applications. As requirements on bandwidth, gain, power consumption as well as low read-out noise and cost are quite severe, an optimal design strategy of a monolithically integrated solution, i.

In optical communication, however, non integrated detectors are usually employed [ 2 ] - [ 8 ] since the particular indirect energy band properties of Silicon make this semiconductor not very efficient for optical reception at nm wavelength. As Si is the most widely used and low cost semiconductor material in electronics and due to the availability of low-cost nm transmitters, there is yet a great interest and challenge to integrate such receivers.

Some solutions exist but at the price of more costly and complex fabrication processes [ 10 - 16 ]. At the system level, owing to its low dark current pA range [ 17 ], low capacitor 10fF for the photodetector [ 1 ] and possibility to integrate this detector with high-performance low-capacitance transistors, global thin-film SOI monolithically integrated photoreceivers have potentially higher gain and lower noise performances which in turn, as we will show here, can increase the IC-sensitivity and alleviate this requirement on the photodetector itself.

In the blue and UV wavelengths, these diodes achieve a high responsivity [ 17 ] and then combine all the advantages of high speed, low dark current and finally high sensitivity [ 1 ]. We present here a top-down design methodology, fully validated by Eldo circuit simulations [ 20 ] and experimental measurements, which allows to predict and optimize, starting from the speed requirements and the technological parameters, the architecture and performances of the receiver.

Our approach generalizes the one proposed in [ 21 ] to all inversion regimes. In addition our design strategy is based on the g m i d methodology [ 22 ] and allows one to optimize the diode and the transimpedance in a simultaneous way.

In section 2 Optical Receivers Basics , the simple resistor system is first presented as well as its limitations. The transimpedance amplifier is then introduced and its basic theory and concepts such as transimpedance gain, bandwidth and stability are derived. Important parameters to compare transimpedance amplifiers are also discussed as well as architectures most often used in the high speed communication area.

Then in section "Design of Multistage Transimpedance Amplifiers", we present our top-down methodology to design transimpedance amplifiers in the case where the voltage gain of the voltage amplifier used in the TIA is independent of the feedback resistor R f.

This is usually the case when the TIA bandwidth is not too close to the transistors frequency limit f t of a given technology and leads to a multi-stage approach. Our design procedure is then applied to the design of a 3 stages 1GHz bandwidth transimpedance amplifier in a 0. Finally, in section "Single stage Transimpedance Amplifier Modeling", we present a top-down methodology to design transimpedance amplifiers when the voltage gain depends on R f. This is the case for very high-speed single-stage transimpedance amplifiers.

Our design procedure is then applied to the design of a single stage 10GHz bandwidth transimpedance amplifier in a 0. The optical receiver is a key element in the optical link. It performs the optical to electrical conversion. The receiver consists of a photodetector followed by a preamplifier and eventually one or more post-amplifiers. The performance of an optical receiver is mainly determined by the preamplifier - photodiode combination. In high-speed communication links, the two most important specifications are speed and sensitivity.

In many cases, the speed is fixed by the application, while the sensitivity has to be maximized. The ultimate limitation is noise. The main noise sources are the photodiode and the preamplifier. In a good design, the latter contribution is minimal. Little noise is added when no active components are used in the preamplifier. This is the case for the simplest preamplifier possible presented in fig.

In this figure, the simple receiver is followed by a buffering amplifier with gain A. Its major drawback is the limited maximal achievable bandwidth when low noise is important. For an input current i ph , the output voltage of the simple optical receiver of fig. The bandwidth of this simple receiver is thus given by:. The bandwidth is limited by C ph which is often much bigger than C inA and the transimpedance-gain R L of the very first stage. As a result, the required bandwidth constrains the maximal transimpedance-gain R L and accordingly the achievable sensitivity of this receiver.

Indeed, the equivalent input noise current spectral density of this front-end is given by [ 21 ]:. The noise of the latter is concentrated in the equivalent spectral density voltage source at the gate of the input transistor, Svg Amp.

As the noise is inversely proportional to R L , low-noise operation implies that the pole is located at a relatively low frequency. This receiver is therefore not suitable for high speed communication applications. To achieve high speed in combination with a large resistor, the latter is used as a feedback resistor with an inverting voltage amplifier.

The resulting structure is a transimpedance amplifier. The transimpedance amplifier TIA fig. It is based on an inverting voltage amplifier with open-loop gain A and a feedback resistor R f to convert and amplify the input current i ph from a photodiode to an output voltage v out. The transimpedance amplifier is a circuit with shunt-shunt feedback. As a general rule, this reduces both the amplifier input and output impedances by the loop-gain of the amplifier [ 23 ].

In turn, this reduction of input impedance allows one for improving the sensitivity and speed trade-off, we faced in the simple resistor amplifier. In this section, various important aspects of transimpedance amplifiers are analyzed. To analyze the TIA frequency behavior, the most important capacitors have been included in fig.

The total input capacitance of the circuit C inT consists of the photodiode capacitance C ph , eventually with its associated parasitics, and the voltage amplifier input capacitance C inA.

The output capacitance C outT is the sum of the amplifier output capacitance C outA and the input capacitance of the subsequent stage, C next. The closed-loop transimpedance-gain is given by:. For a well designed voltage amplifier with sufficiently large gain A and small output impedance R out this can be simplified to:.

This compares well with the simplified transfer function of a system with two well separated real poles p 1 and p 2 , which is given by [ 24 ]:. The TIA dominant pole p 1 can theoretically be situated either at the input or at the output node. In between those two extreme cases, both poles approach each other and give rise to a complex conjugated pole pair. This intermediate poles placement is best avoided as it results in a bump in the frequency response with overshoot and long settling times of the transients [ 24 ] see also fig.

In the case of high speed circuits where the diode capacitance C ph usually dominates the other capacitances and where we try to have the resistance R f value as high as possible to increase the transimpedance-gain, the dominant pole is usually located at the input node and the transimpedance bandwidth is then given by:. Comparing this bandwidth with that given by the simple resistor amplifier one eq.

This means that for a given bandwidth, a TIA will have a transimpedance gain increased by A compared to the simple resistor amplifier. To be stable the gain A has however to be constrained, as we will see below. As the transimpedance amplifier contains a feedback loop, its stability has to be assured. To analyze this problem, the shunt-shunt feedback amplifier is presented by its equivalent circuit of fig. From this figure, the open-loop gain and the feedback factor are easily derived:.

To obtain a stable system, the non-dominant pole of the amplifier loop gain has to be sufficiently higher than the 0 dB crossing frequency, which is given the dominant pole is assumed at the input node by:. The latter is equal to the TIA closed-loop bandwidth Eq. Actually, the equivalence of these two equations demonstrates that a TIA behaves as a voltage amplifier in unity-gain feedback configuration.

The stability analysis of both structures is therefore identical [ 21 ]. To achieve a reasonable phase-margin, non-dominant poles have to be sufficiently higher than the receiver bandwidth. This implies for the second pole in this structure [ 24 ]:.

In general, some extra poles may be present on the internal nodes of the voltage amplifier. These must obviously also be considered during the design and be placed at sufficiently high frequencies to guarantee stability. These requirements ultimately limit the maximal achievable transimpedance-gain and bandwidth.

To summarize, the transimpedance amplifier allows one, owing to its feedback mechanism, to increase the frequency of the dominant pole to a value that is A times higher that the one we would have with a simple resistor. However, by increasing the gain A, the dominant pole approaches the second pole.

In order to avoid stability problems, we have to limit the gain A such that the dominant pole stays around 3 times smaller that the second pole the factor 3 corresponds to the classical 60 phase margin condition in open loop configuration.

In analogy with the gain-bandwidth product used for an amplifier, the transimpedance-gain R f - bandwidth BW trans product or ZBW has been proposed as the parameter that measures both the speed and the sensitivity performance of the transimpedance amplifier [ 21 ]:. In a given device, ZBW is a constant.

This tells us that, to some extent, transimpedance gain can simply be traded for bandwidth and vice-versa by tuning the feedback resistor. This substitution is only limited by stability considerations. The maximal achievable bandwidth has to be a factor smaller than the first non-dominant pole of the receiver to maintain sufficient phase-margin. This factor of merit also emphasizes the need in critical high speed applications for photodiodes integrated on chip along with the receivers which can reduce the photodiode capacitance drastically by a factor up to ten times by removing the bonding capacitor.

SOI has here an advantage over other Si integrated technologies for high speed applications e. Transimpedance amplifier may differ by the kind of voltage amplifiers they use. In the high-speed communications field, two amplifier architectures are mostly used: the single transistor voltage amplifier STVA and the CMOS inverter used as an amplifier. A three stages TIA version of both cases is shown in fig. The inverter case has the advantage of auto biasing the current depends on the gate voltage and the size of the P and NMOS transistor and then requires no additional bias circuit.

In very high speed applications, in order to improve crosstalk immunity, differential versions of the transimpedances are also employed and then differential pairs or two single inverters with a dummy branch can be used [ 26 ], [ 27 ] and [ 7 ].

One can distinguish different type of TIAs by their number of stages. Typical designs use either a single-stage or multi-stage approach. It can be shown [ 21 ] and will be further developed that applications requesting a high bandwidth compared to the technology's f t are limited to single-stage amplifiers as there is no room for placing the extra poles that are inevitably introduced by the multiple-stage designs.

However, for frequencies at least 20 to 30 times lower than f t , a multi-stage design is the way to go. We will now describe our methodology to optimize the stages number N that maximizes the voltage gain in transimpedance amplifiers based on N identical STVA amplifiers.

The gain of a single SVTA stage is given by:. In the case of the amplifier of figure 3a, we have:. For the single stage amplifier, with the dominant pole at the input and only one non-dominant pole at the output, the condition of stability was given by eq. In the case of a multi-stages amplifier, we now have a multiple pole roll-off. To achieve same phase margin with a N pole roll-off than with a single pole, we must now place each of these N poles at a frequency X N.

X A higher than the dominant pole frequency.

Electronic Design - From Concept to Reality

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Degree in Computer Engineering

Single amplifier forming a section of the cascaded amplifier circuit. During the height of car audio, many considered the increasing size of subwoofers as the next breakthrough in sound output SPL. But, like nearly all things in the field of electronics, advancements are staggered due to current ancillary limitations. The increase in driver size created the need for an increase in amplifier power. However, the amplifier technology at the time did not match the pace of the advancement and subsequent increase in subwoofer size. This introduced the car audio world to daisy-chaining cascading to accommodate the need for increased amplifier output. Daisy-chaining cascading amplifiers in the field of car audio is no longer necessary due to the advancement in amplifier technology, i. In other areas within the field of electronics, cascading is still a requirement. As you may know, a cascade amplifier is a two-port network comprised of a series of amplifiers in which each amplifier connects sends its output to the input of the next amplifier in the chain. This complicates gain calculations for these cascaded stages due to the loading between the stages or.

Electronic devices

Make sure you stand out with an international, tech-focused vision, with study placements abroad in Shanghai and San Francisco. Have a basic general knowledge of the studied area. Acquire a capacity for analysis and synthesis in the study and design of analog circuits. Acquire the capacity for organization and planning in systems design. Use software techniques and new tools in systems design 5.

ECE 320 - Linear Active Circuit Design (3)

Try out PMC Labs and tell us what you think. Learn More. High-resolution electronic interface circuits for transducers with nonlinear capacitive impedance need an operational amplifier, which is stable for a wide range of load capacitance. Such operational amplifier in a conventional design requires a large area for compensation capacitors, increasing costs and limiting applications. In order to address this problem, we present a gain-boosted two-stage operational amplifier, whose frequency response compensation capacitor size is insensitive to the load capacitance and also orders of magnitude smaller compared to the conventional Miller-compensation capacitor that often dominates chip area.

If All Else Fails, Read This Article. Avoid Common Problems When Designing Amplifier Circuits

This is part 10 of a tutorial on fiber amplifiers from Dr. The tutorial has the following parts:. It has been mentioned already in previous parts of this tutorial, e. Fiber amplifier systems often provide a very high gain of several tens of decibels. This implies that different parts of the active fiber s see very different amounts of optical powers or pulse energies. There are then several reasons why a large mode area is needed for the last stage a power amplifier stage :. Typically, the power amplifier stage has a substantially lower gain but provides the largest part of the output power.

Final Exam - Fall 2009 Time allowed:-3 hrs Electronics I January 21 ...

Hello friends, I hope you all are doing great. There are numerous types of amplifier circuits like common emitter amplifier , common base amplifier, common collector amplifier , differential amplifier. All these amplifiers we discussed in the detail in a previous tutorial. About two-stage capacitively coupled amplifier we discussed with detail in a multistage amplifier.

When I used to play guitar, I quickly realized the last thing you should do is connect your amplifiers together. In your electronic circuits, you can daisy chain your amplifiers into a cascaded amplifier to increase an input signal to a higher level at the output. With any multistage amplifier, there is a question of the cascaded amplifier gain and saturation points that can be reached in these circuits without producing distortion. In addition, noise at the input can be propagated to the output, where it also experiences gain. These components are packaged in individual ICs and have the familiar triangular symbol in a circuit diagram or schematic.

Jump to navigation. Integrated theory and design laboratory course. Current mirrors, active loads, multistage amplifiers, output stages, frequency response and feedback with emphasis on design, simulations of design and laboratory verification, measurement techniques and technical communications. Students completing this course should be able to design and use basic analog building blocks and understand how they interact using the operational amplifier as an example. The emphasis in the lectures is on developing recognition of the interplay between large-signal and small-signal behavior, on learning the constraints each place on the other, and upon using multiple stages to circumvent these problems. ECE A contributes directly to the following specific electrical and computer engineering student outomes of the ECE department:.

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