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# Great God: The scheme is calculated

2023-03-22【Archive】

**Click on image above to go to article about 9th Anniversary Event**

**Before you read this article, I would like to make a few clarifications:**

(1) I recently read Razavi's book and wrote down these things. This is just a summary of my personal learning process. If you have any opinions, you can chat with each other;(2) Keep thinking , Continuous understanding, continuous summary! I hope everyone sticks to it!

**0****11**

**CS single-tube amplifier circuit**

The common-source single-transistor amplifier circuit is mainly used to achieve linear amplification of small input signals, that is, to obtain a higher voltage gain. In DC analysis, static operating point of circuit can be provided according to DC gate input voltage, and according to IV curve of MOSFET, static operating point of MOSFET has a wide dynamic range, which mainly appears as a MOSFET tube in VDS has a wide range of values. When amplifying small signals, minimum input voltage is VIN-VTH, and maximum value is about VDD. It is assumed that it can fully express linear characteristics in saturation region and achieve maximum signal gain [under ideal conditions], a certain static operating point is about VDS=(VIN-VTH VDD)/2, but actual CS circuit characteristics and non-linear relationship exhibited by MOS Tube limits ideal amplification of weak signals.

Basic manifestations:【1】The gain that circuit can detect in saturation region is relatively large, but still limited, that is, it is in allowable range of input signal, Determines gain of circuit. The non-linearity of circuit and inconsistency of slope of MOS tube determine that gain of a small input signal by CS circuit is limited as a constant, gain of circuit is determined approximately.

【2】CS circuit also reflects two general gain characteristics of analog CMOS circuit. First, static operating point of circuit will directly affect gain characteristics of small signals, that is, DC characteristics. interaction between it and its communication characteristics. From characteristic curve shown by input-output characteristics, it can be seen that circuit gain corresponding to different points in saturation region of MOSFET is different, which depends on non-linear characteristics of device, but non-linearity can be approximated to linearity in a fairly small range. This shows that coefficient The gain of circuit is directly related to static operating point of circuit, with an approximate linearization of various portions of curve.It can be seen that difference in circuit's static operating point will determine circuit's own gain. This is reflected in calculation. The conductivity of CS circuit depends on quiescent current generated at different gate voltages, so circuit gain is not necessary, but gain selectivity will indirectly limit output voltage swing. All of this reflects a tension between choice of amplifier circuit gain and other factors such as current, power consumption, and speed. 【3】Secondly, static operating point of circuit will directly affect DC characteristics of previous and subsequent stages, since gain achieved by CS circuit is aimed at amplifying small signals. However, gain characteristics of circuit are based on determination of static operating point. In other words, intermediate CS circuit in circuit must determine operating point of current stage according to static output of previous stage, which causes effect on last stage to increase complexity of circuit design. However, CD circuit in circuit design can realize DC level shift characteristic and following AC signal characteristic, which also eliminates influence between static stages. Generally speaking, this simplifies design but increases circuit area. 【4】Analysis Method: The complex characteristics of analog CMOS circuits also define a special circuit small-signal analysis method, which is different from BJT. The first method starts directly from large-signal analysis. The analog IC mainly operates in linear region and saturation region, combined with ratio of current and voltage in various regions determined by gate voltage and drain-source voltage of MOSFET, to determine performance of a large signal circuit. and large signal characteristic curve can be determined on one hand. The static operating point of circuit, on other hand, also indirectly reflects characteristics of AC circuit, because analysis of characteristics of circuit from large signal to small signal is to realize a non-linear linear analysis of circuit, and AC characteristic or characteristic of a small signal is a small change Quantitative analysis, and characteristics of large signals are full-scale analysis or general analysis. Therefore, a small signal is an approximation to a large signal near operating point, a kind of linearization. In other words, analysis from a large signal to a small signal is expressed as a differential dependence in mathematics. The second method is similar to small signal equivalent model analysis in BIT analysis. Therefore, equivalent signal model set at device level can only provide a simple calculation method at circuit level and cannot provide an intuitive understanding of circuit. Therefore, in low-frequency state, theThe performance is as follows: CS circuit can realize input voltage gain, its voltage gain is high, input impedance is infinite, and output impedance is small. 【5】The MOS tube diode is equivalent to a low impedance device. As a general load, it replaces resistor to amplify small signals, but gain of circuit is limited. In general, using an active diode composed of a resistor or a MOS lamp as a load cannot provide high gain gain characteristics. 【6】Common-source amplifier circuit with current source load realizes high voltage gain amplification and large output swing of circuit, but to a certain extent it also creates new problems. that high gain is due to large equivalent output impedance, and large output swing can be realized by adjusting minimum operating voltage of static NMOS and PMOS, but capacitive influence of GD and high output impedance result in a slow response speed of circuit. The circuit can provide better voltage conversion in low frequency operating state, but circuit speed is limited in high frequency operating region. On other hand, high-gain characteristic of circuit results in a large drain-to-source voltage spread at output, which requires that output drain voltage be equal to half sum of NMOS and PMOS voltages at critical static saturation point. Thus, output swing is guaranteed will be symmetrical without distortion, which requires gate input voltage of circuit to be more stable in a static state, that is, drain output voltage is half sum of voltages at critical saturation point. 【7】Misunderstanding: The operating voltage of each point of circuit is determined in static state. For example, in a CS circuit with a load, current source voltage of drain-source amplifier lamp has a large range of change when operating in saturation region, but when circuit is operating, its quiescent current is equal, and voltage of drain terminal is same, so static output of drain terminal can be uniquely determined point where input is unique, reflecting unique drain voltage. As a result of this analogy, in a complex circuit made up of MOSFETs, it is possible to determine drain voltage of each MOSFET in saturation. 【8】Negative CS circuit source level feedback. The introduction of negative feedback has caused a fundamental change in structure of circuit, which means that a feedback network consisting of passive devices will be connected to gate input voltage and drain output voltage, so as depth of feedback increases, amount of change in input signal will be mainly reflected in feedback resistance, that is, a change in small input signal will mainly be reflected in feedback resistancefeedback resistance The effect of this feedback weakens non-linear relationship between IDS and VGS and approximates a linearization. In this case, equivalent circuit steepness will also be limited by introduction of feedback. On one hand, negative feedback changes linearity of circuit, on other hand, it increases stability of gain, but improvement of these characteristics is based on a decrease in voltage gain.

**0****2**

**Single-tube CD/CG amplifier circuit**

The source follower is mainly used in circuit to provide voltage buffering and level shifting. The main manifestations are: voltage gain of circuit is approximately 1, so that output roughly follows input; change between output and input under saturation conditions: output voltage is equal to input voltage - threshold voltage; input impedance of circuit tends to infinity, and output impedance is very small, so that circuit can drive a smaller load in order to maintain circuit's structural consistency. Therefore, CD circuit shows DC level shift characteristic in a large signal and following AC signal characteristic in a small signal. The relatively low input impedance of CG circuit is used in circuit to achieve matching performance.

**0****3**

Cascode diagram

The cascode sleeve structure limits output voltage swing to a certain extent, that is, minimum output of circuit must allow cascode MOSFET to operate in saturation, that is, minimum output voltage The level is approximately equal to sum of two overload voltages, but it significantly increases output impedance of circuit. The cascode structure converts input voltage signal into current, and current is used as input of CS circuit. The folded cascode structure exhibits best low-voltage performance when implementing circuit amplification.

**0****4**

**Scheme calculated**

【1】The definition of DC operating point is determined by its input quiescent voltage or quiescent current. In other words, it is possible to calculate quiescent voltage and current of each point in circuit, because IV of each point in rest circuit ratio satisfies basic circuit theorem, and expressions for current and voltage, expressed by various circuit structures, are uniquely determined, that is, static parameters of circuit are uniquely determined.

【2】AC analysis based on DC operating point is an analysis of input small signal, and gain achieved is to amplify small signal superimposed on operating point. In other words, DC level provides steady-state conditions for small signal operation, while AC characteristics reflect dynamic conversion of signal.nal, that is, gain characteristics, so that small AC signals superimposed on DC level act as inputs to circuit to achieve signal amplification. In general, AC characteristics of a circuit can be obtained by small-signal analysis, or analysis can be simplified by an equivalent circuit model, so that gain, input impedance, and output impedance of circuit can be calculated.

**05**

**Intuitive understanding of MOSFET small signal model**

The operating state of a MOSFET under saturation conditions can be analyzed using a small signal equivalent circuit, but small signal equivalent circuit analysis provides only a relatively simplified calculation method. The MOS lamp in circuit converts a small change in gate-to-source voltage into a change in drain-to-source current, and an AC output voltage can be generated by passing through an appropriate load in AC path and superimposing DC. and alternating current produces a finite output voltage, as a result of which root of phenomenon lies in non-linear characteristics of device. Therefore, an analysis of DC path can be obtained according to relationship between its static operating voltage and current, and an AC equivalent circuit can be set for AC path, but for active devices, non-linearity of current and voltage leads to device itself Impedance separation ac and dc, resulting in changes in some of parameters of ac path, so when analyzing an ac circuit, attention should be paid to change in impedance of device, which is separation of ac and dc impedance. caused by non-linearity of active devices. From small signal MOSFET equivalent circuit, it can be seen that gate-source voltage plays a leading role in controlling drain-source current, that is, influence of drain-source The influence of voltage and substrate on operating state of device can be ignored. Therefore, it can be seen that drain-to-source current of a MOSFET is affected by three aspects. From point of view of gate port, effect of gate voltage on current is gm*vgs, effect of drain-source voltage on current is gd*vds, and effect of substrate is gmb*vbs. Then from current point of view, secondary effect is expressed as sum of currents gm*vgs, gd*vds and gd*vds. Under normal conditions, influence of channel length modulation and body effect is ignored in initial circuit analysis, so simplified MOS model is only affected by gate voltage, so equivalent resistance from source to gate is about 1/gm. Simplified circuit analysis is often error prone due to neglected spillovers, but an intuitive understanding of circuit is important.

**0****6**

**SPICE Model**

The connection at transistor level determines structure of circuit, butThe performance of circuit depends on specific parameter settings. The SPICE model provides a specific device parameterization process, that is, circuit simulation analysis needs to set parameters, that is, various parameters limited in process provide a relatively complete model of device-level parameters, such as channel length modulation factor, parasitic capacitance, oxide layer thickness gate, etc. are all used to quantify transistor parameters, meaning some device-level parameters can also be calculated!

**0****7**

**Five-pipe differential pair (fully symmetrical structure)**

The input signal is a superposition of DC and AC. The DC level is used to determine static operating point of circuit. According to I-V curve, linearity of basic differential structure is best under condition that input DC level is equal and its linear range is largest, which increases dynamic range of small AC input signal. However, choice of DC operating point depends on basic structure of circuit, and also has a certain range: make sure that tail current tube is in saturation region and at same time cannot force amplifier tube to enter linear region. , so that input common-mode level selection range is approximately defined. The current and voltage of nodes of a five-lamp differential pair under static conditions can be calculated completely. The circuit's symmetrical structure makes it easy to analyze its AC characteristics, and basic five-tube differential pair can be simplified as a single-tube CS amplifier circuit.

The fully symmetrical five-lamp differential pair also once again reflects characteristic of analog CMOS circuits, mutual influence between AC and DC. In other words, DC level of basic CS circuit determines static operating point of circuit, but maximum output level when operating at DC also limits output voltage of small AC signal, that is, gain is limited, provided that input of circuit is defined. Or, small signal input swing is limited provided that gain is defined. In short, AC and DC characteristics of a circuit have a large influence on each other, which is different from BIT.

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