CN109889165B - Amplifier with adjustable output common-mode voltage - Google Patents
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Abstract
Description
技术领域technical field
本发明涉及一种输出共模电压可调节放大器,属于可编程增益放大器技术领域。The invention relates to an amplifier with adjustable output common-mode voltage, belonging to the technical field of programmable gain amplifiers.
背景技术Background technique
在射频接收系统中,可编程增益放大器是无线通信模块中的重要部分,主要用于拓展接收信号的动态范围,以改善接收链路的整体性能。其根据输入信号的强度调节信号的放大增益,使得输出信号幅度恒定,以保证接收机能够正确解调接收信号。In the radio frequency receiving system, the programmable gain amplifier is an important part of the wireless communication module, which is mainly used to expand the dynamic range of the received signal to improve the overall performance of the receiving chain. It adjusts the amplification gain of the signal according to the strength of the input signal, so that the amplitude of the output signal is constant, so as to ensure that the receiver can correctly demodulate the received signal.
为使输出信号幅度恒定,其中一种方法便是引入主从结构得到恒定的跨导。鉴于此,可编程增益放大器的功耗水平在接收链路中占据了可观的份额。为了实现整体接收电路的低功耗,随着工艺的进步,采取更低的电源电压进行设计。然而在低电压下,因输出共模电压过高而影响下一级电路尾电流源的性能。In order to make the output signal amplitude constant, one of the methods is to introduce a master-slave structure to obtain a constant transconductance. For this reason, the power consumption level of the programmable gain amplifier occupies a considerable share in the receive chain. In order to realize the low power consumption of the overall receiving circuit, with the progress of the technology, a lower power supply voltage is adopted for design. However, under low voltage, the performance of the tail current source of the next stage circuit is affected due to the high output common-mode voltage.
传统的差分放大器在输入共模电平一定的情况下,输出共模电压无法随着电源电压变化而自适应调节。在可编程增益放大器中,为了得到随温度变化增益变化较小的目的,经常采用主从结构得到恒定跨导,这就需要对自偏置负载放大器的输出端进行误差采样。在低电压情况下,当自偏置负载放大器的输出端共模电压较高时,误差采样电路的尾电流源源漏电压小,从而无法保证电路正常工作。In a traditional differential amplifier, when the input common-mode level is constant, the output common-mode voltage cannot be adaptively adjusted as the power supply voltage changes. In a programmable gain amplifier, in order to obtain a small change in gain with temperature, a master-slave structure is often used to obtain a constant transconductance, which requires error sampling at the output of the self-biased load amplifier. In the case of low voltage, when the common-mode voltage of the output terminal of the self-biased load amplifier is high, the source-to-drain voltage of the tail current source of the error sampling circuit is small, so that the normal operation of the circuit cannot be guaranteed.
发明内容Contents of the invention
本发明所要解决的技术问题在于克服低电压低功耗设计中共模电压过高的问题,提供一种输出共模电压可调节放大器,其将电源电压的变化转化为偏置电流的变化,从而自适应调节输出共模电压的大小。其适用于低电压低功耗下可编程增益放大器等应用场合。The technical problem to be solved by the present invention is to overcome the problem of high common-mode voltage in low-voltage and low-power Adapt to adjust the size of the output common-mode voltage. It is suitable for applications such as programmable gain amplifiers under low voltage and low power consumption.
本发明具体采用以下技术方案解决上述技术问题:The present invention specifically adopts the following technical solutions to solve the above technical problems:
一种输出共模电压可调节放大器,包括自适应电流偏置级、共模电压调节电路以及自偏置负载放大器;所述自偏置负载放大器,用于在两个NMOS管之间构成虚地点并为之提供栅极偏置电压,同时提供增益并与共模电压调节电路复用负载电阻;所述自适应电流偏置级利用放大器将电阻一端箝位到参考电压,当电源电压变化时电源电压的变化量全部体现在电阻上并相应转化为偏置电流变化量;所述共模电压调节电路中的参考电流源被偏置电流抽拉后所剩余电流流经共模电压调节电路中的负载电阻形成自适应压降,实现输出共模电压调节。An adjustable output common-mode voltage amplifier, including an adaptive current bias stage, a common-mode voltage regulation circuit, and a self-biased load amplifier; the self-biased load amplifier is used to form a virtual point between two NMOS tubes And provide gate bias voltage for it, provide gain and multiplex the load resistance with the common mode voltage regulation circuit at the same time; The adaptive current bias stage uses the amplifier to clamp one end of the resistance to the reference voltage, when the power supply voltage changes The amount of change is all reflected in the resistance and correspondingly converted into the amount of bias current change; after the reference current source in the common-mode voltage regulation circuit is drawn by the bias current, the remaining current flows through the load in the common-mode voltage regulation circuit The resistors form an adaptive voltage drop for output common-mode voltage regulation.
进一步地,作为本发明的一种优选技术方案:所述自适应电流偏置级包括第一放大器、第一电阻、第一NMOS管、第二NMOS管;其中,参考电压连接第一放大器的负输入端,第一放大器的正输入端连接第一电阻的负端,且第一放大器的输出端连接第一NMOS管的栅极;所述第一NMOS管的源极接地且漏极连接第一电阻的负极;所述第二NMOS管的栅极连接第一NMOS管的栅极,第二NMOS管的源极接地且漏极与参考电流源的负极相连;所述第一电阻的正极与电源相连。Further, as a preferred technical solution of the present invention: the adaptive current bias stage includes a first amplifier, a first resistor, a first NMOS transistor, and a second NMOS transistor; wherein, the reference voltage is connected to the negative Input terminal, the positive input terminal of the first amplifier is connected to the negative terminal of the first resistor, and the output terminal of the first amplifier is connected to the gate of the first NMOS transistor; the source of the first NMOS transistor is connected to the ground and the drain is connected to the first The negative pole of the resistor; the gate of the second NMOS transistor is connected to the gate of the first NMOS transistor, the source of the second NMOS transistor is grounded and the drain is connected to the negative pole of the reference current source; the positive pole of the first resistor is connected to the power supply connected.
进一步地,作为本发明的一种优选技术方案:所述共模电压调节电路包括参考电流源、第二电阻、第三电阻;所述参考电流的正端与电源相连,参考电流的负端分别与第二电阻的负端、第三电阻的负端相连;所述第二电阻和第三电阻的正端分别连接至自偏置负载放大器。Further, as a preferred technical solution of the present invention: the common-mode voltage regulation circuit includes a reference current source, a second resistor, and a third resistor; the positive terminal of the reference current is connected to a power supply, and the negative terminals of the reference current are respectively It is connected to the negative terminal of the second resistor and the negative terminal of the third resistor; the positive terminals of the second resistor and the third resistor are respectively connected to a self-biased load amplifier.
进一步地,作为本发明的一种优选技术方案:所述自偏置负载放大器包括第一PMOS管、第二PMOS管、第三PMOS管、第三NMOS管、第四NMOS管;其中,所述第三PMOS管的栅极连接反馈电压且源极接电源,第三PMOS管的漏极分别与第一PMOS管的源极、第二PMOS管的源极相连;所述第一PMOS管的栅极连接输入电压正端,且第一PMOS管的漏极连接第三NMOS管的漏极;所述第三NMOS管的栅极连接共模电压调节电路且源极接地;所述第二PMOS管的栅极连接输入电压负端,且第二PMOS管的漏极连接第四NMOS管的漏极;所述第四NMOS管的栅极与第三NMOS管的栅极相连,且第四NMOS管的源极接地。Further, as a preferred technical solution of the present invention: the self-biased load amplifier includes a first PMOS transistor, a second PMOS transistor, a third PMOS transistor, a third NMOS transistor, and a fourth NMOS transistor; wherein, the The gate of the third PMOS transistor is connected to the feedback voltage and the source is connected to the power supply, and the drain of the third PMOS transistor is respectively connected to the source of the first PMOS transistor and the source of the second PMOS transistor; the gate of the first PMOS transistor The pole is connected to the positive terminal of the input voltage, and the drain of the first PMOS transistor is connected to the drain of the third NMOS transistor; the gate of the third NMOS transistor is connected to the common mode voltage regulation circuit and the source is grounded; the second PMOS transistor The gate of the second PMOS transistor is connected to the negative terminal of the input voltage, and the drain of the second PMOS transistor is connected to the drain of the fourth NMOS transistor; the gate of the fourth NMOS transistor is connected to the gate of the third NMOS transistor, and the fourth NMOS transistor The source is grounded.
本发明采用上述技术方案,能产生如下技术效果:The present invention adopts above-mentioned technical scheme, can produce following technical effect:
本发明的输出共模电压可调节放大器,由于自适应电流偏置级采用放大器将电阻一端箝位到参考电压,当电源电压变化时,电源电压的变化量全部体现在电阻上,并相应转化为偏置电流变化量;参考电流源被偏置电流抽拉后所剩余电流流经放大器负载形成自适应压降,实现了输出共模电压可调节的功能。该电路利用放大器将电阻一端固定在参考电位,当电源电压变小时,电阻上的压降降低,也就意味着流经电阻的电流减小。由于放大器的虚短虚断特性,该电流无法流过放大器输入端,故全部流经偏置第一NMOS管MN1,意味着镜像偏置第二NMOS管MN2从参考电流源抽取电流减少,放大器负载电阻上有更多压降,从而实现低电源电压情况下输出共模电压更低,更易于与下级误差采样电路级联。The output common-mode voltage adjustable amplifier of the present invention, because the self-adaptive current bias stage uses the amplifier to clamp one end of the resistance to the reference voltage, when the power supply voltage changes, the variation of the power supply voltage is all reflected on the resistance, and correspondingly converted into The amount of bias current variation; the remaining current after the reference current source is pulled by the bias current flows through the amplifier load to form an adaptive voltage drop, which realizes the adjustable output common-mode voltage. This circuit uses an amplifier to fix one end of the resistor at a reference potential. When the power supply voltage becomes smaller, the voltage drop across the resistor decreases, which means that the current flowing through the resistor decreases. Due to the virtual short and virtual break characteristics of the amplifier, the current cannot flow through the input terminal of the amplifier, so it all flows through the biased first NMOS transistor MN1, which means that the mirror biased second NMOS transistor MN2 draws less current from the reference current source, and the amplifier load There are more voltage drops on the resistors, so that the output common-mode voltage is lower under the condition of low power supply voltage, and it is easier to cascade with the lower-level error sampling circuit.
因此,本发明的放大器可将电源电压的变化转化为偏置电流的变化,从而调节输出共模电压的大小,显著提高了低电压设计下后级电路尾电流源的漏源电压,提高电路的性能;本发明解决了在低电压低功耗可编程增益放大器PGA链路,主从结构中主级自偏置负载放大器输出共模电压过高使得误差采样电路尾电流源无法正常工作的问题,因此本发明适用于低电压低功耗下可编程增益放大器等应用场合。Therefore, the amplifier of the present invention can convert the change of the power supply voltage into the change of the bias current, thereby adjusting the size of the output common-mode voltage, significantly improving the drain-source voltage of the tail current source of the subsequent stage circuit under the low-voltage design, and improving the circuit performance. Performance; the present invention solves the problem that the error sampling circuit tail current source cannot work normally due to the high output common-mode voltage of the master-level self-bias load amplifier in the master-slave structure in the low-voltage and low-power programmable gain amplifier PGA link. Therefore, the present invention is suitable for applications such as programmable gain amplifiers under low voltage and low power consumption.
附图说明Description of drawings
图1为本发明输出共模电压可调节放大器的电路图。FIG. 1 is a circuit diagram of an amplifier with an adjustable output common-mode voltage in the present invention.
图2为本发明的放大器应用于可编程增益放大器中增益随温度变化的曲线图。Fig. 2 is a graph showing the variation of gain with temperature when the amplifier of the present invention is applied to a programmable gain amplifier.
图3为本发明应用于可编程增益放大器链增益随温度变化的曲线图。Fig. 3 is a graph showing the variation of the gain of the programmable gain amplifier chain with temperature according to the present invention.
具体实施方式detailed description
下面结合说明书附图对本发明的实施方式进行描述。Embodiments of the present invention will be described below in conjunction with the accompanying drawings.
如图1所示,本发明设计了一种输出共模电压可调节放大器,包括自适应电流偏置级、共模电压调节电路以及自偏置负载放大器;所述自适应电流偏置级负责将电源电压变化转化为偏置电流变化;所述共模电压调节电路间接对该偏置电流做电流和电压变换;所述自偏置负载放大器则负责提供增益。具体地,所述自偏置负载放大器,用于在两个NMOS管之间构成虚地点并为之提供栅极偏置电压,同时提供增益并与共模电压调节电路复用负载电阻;所述自适应电流偏置级利用放大器将电阻一端箝位到参考电压,当电源电压变化时电源电压的变化量全部体现在电阻上并相应转化为偏置电流变化量;所述共模电压调节电路中的参考电流源被偏置电流抽拉后所剩余电流流经共模电压调节电路中的负载电阻形成自适应压降,实现输出共模电压调节。As shown in Fig. 1, the present invention has designed a kind of output common-mode voltage adjustable amplifier, comprises adaptive current bias stage, common-mode voltage regulation circuit and self-biased load amplifier; Described adaptive current bias stage is responsible for The variation of the power supply voltage is converted into the variation of the bias current; the common-mode voltage regulation circuit indirectly converts the current and voltage of the bias current; the self-biased load amplifier is responsible for providing gain. Specifically, the self-biased load amplifier is used to form a virtual point between two NMOS transistors and provide a gate bias voltage for it, and at the same time provide gain and multiplex a load resistance with a common-mode voltage regulation circuit; the self-biased load amplifier The adaptive current bias stage uses an amplifier to clamp one end of the resistor to the reference voltage, and when the power supply voltage changes, the variation of the power supply voltage is all reflected on the resistor and correspondingly converted into a variation of the bias current; the common-mode voltage regulation circuit After the reference current source is drawn by the bias current, the remaining current flows through the load resistance in the common-mode voltage regulation circuit to form an adaptive voltage drop, thereby realizing the regulation of the output common-mode voltage.
具体地,所述自适应电流偏置级包括第一放大器A1、第一电阻R1、第一NMOS管MN1、第二NMOS管MN2;其中,参考电压连接第一放大器A1的负输入端,第一放大器A1的正输入端连接第一电阻R1的负端,且第一放大器A1的输出端连接第一NMOS管MN1的栅极;所述第一NMOS管MN1的源极接地且漏极连接第一电阻R1的负极;所述第二NMOS管MN2的栅极连接第一NMOS管MN1的栅极,第二NMOS管MN2的源极接地且漏极与参考电流源的负极相连;所述第一电阻R1的正极与电源相连。Specifically, the adaptive current bias stage includes a first amplifier A1, a first resistor R1, a first NMOS transistor MN1, and a second NMOS transistor MN2; wherein, the reference voltage is connected to the negative input terminal of the first amplifier A1, and the first The positive input terminal of the amplifier A1 is connected to the negative terminal of the first resistor R1, and the output terminal of the first amplifier A1 is connected to the gate of the first NMOS transistor MN1; the source of the first NMOS transistor MN1 is connected to the ground and the drain is connected to the first The negative pole of the resistor R1; the gate of the second NMOS transistor MN2 is connected to the gate of the first NMOS transistor MN1, the source of the second NMOS transistor MN2 is grounded and the drain is connected to the negative pole of the reference current source; the first resistor The positive pole of R1 is connected to the power supply.
所述共模电压调节电路包括参考电流源、第二电阻R2、第三电阻R3;所述参考电流的正端与电源相连,参考电流的负端分别与第二电阻R2的负端、第三电阻R3的负端相连;所述第二电阻R2和第三电阻R3的正端分别连接至自偏置负载放大器,即所述第二电阻R2的正端连接自偏置负载放大器中第一PMOS管MP1的漏极;第三电阻R3的正端连接自偏置负载放大器中第二PMOS管MP2的漏极。The common-mode voltage regulation circuit includes a reference current source, a second resistor R2, and a third resistor R3; the positive end of the reference current is connected to the power supply, and the negative end of the reference current is connected to the negative end of the second resistor R2, the third resistor R2, and the third resistor R2 respectively. The negative terminals of the resistor R3 are connected; the positive terminals of the second resistor R2 and the third resistor R3 are respectively connected to the self-biased load amplifier, that is, the positive terminal of the second resistor R2 is connected to the first PMOS in the self-biased load amplifier The drain of the transistor MP1; the positive end of the third resistor R3 is connected to the drain of the second PMOS transistor MP2 in the self-biased load amplifier.
所述自偏置负载放大器包括第一PMOS管MP1、第二PMOS管MP2、第三PMOS管MP3、第三NMOS管MN3、第四NMOS管MN4;其中,所述第三PMOS管MP3的栅极连接反馈电压且源极接电源,第三PMOS管MP3的漏极分别与第一PMOS管MP1的源极、第二PMOS管MP2的源极相连;所述第一PMOS管MP1的栅极连接输入电压正端,且第一PMOS管MP1的漏极连接第三NMOS管MN3的漏极,所述第二电阻R2的正端与第三NMOS管MN3的漏极以及第一PMOS管MP1的漏极相连;所述第三NMOS管MN3的栅极连接共模电压调节电路中第二电阻R2的负端,且第三NMOS管MN3的源极接地;所述第二PMOS管MP2的栅极连接输入电压负端,且第二PMOS管MP2的漏极连接第四NMOS管MN4的漏极,所述第三电阻R3的正端与第四NMOS管MN4的漏极以及第二PMOS管MP2的漏极相连,而第三电阻R3的负端与第二电阻R2的负端相连;所述第四NMOS管MN4的栅极与第三NMOS管MN3的栅极相连,且第四NMOS管MN4的源极接地。The self-biased load amplifier includes a first PMOS transistor MP1, a second PMOS transistor MP2, a third PMOS transistor MP3, a third NMOS transistor MN3, and a fourth NMOS transistor MN4; wherein, the gate of the third PMOS transistor MP3 The feedback voltage is connected and the source is connected to the power supply, and the drain of the third PMOS transistor MP3 is respectively connected to the source of the first PMOS transistor MP1 and the source of the second PMOS transistor MP2; the gate of the first PMOS transistor MP1 is connected to the input The positive terminal of the voltage, and the drain of the first PMOS transistor MP1 is connected to the drain of the third NMOS transistor MN3, the positive terminal of the second resistor R2 is connected to the drain of the third NMOS transistor MN3 and the drain of the first PMOS transistor MP1 connected; the gate of the third NMOS transistor MN3 is connected to the negative terminal of the second resistor R2 in the common-mode voltage regulation circuit, and the source of the third NMOS transistor MN3 is grounded; the gate of the second PMOS transistor MP2 is connected to the input voltage negative terminal, and the drain of the second PMOS transistor MP2 is connected to the drain of the fourth NMOS transistor MN4, the positive end of the third resistor R3 is connected to the drain of the fourth NMOS transistor MN4 and the drain of the second PMOS transistor MP2 connected, and the negative end of the third resistor R3 is connected to the negative end of the second resistor R2; the gate of the fourth NMOS transistor MN4 is connected to the gate of the third NMOS transistor MN3, and the source of the fourth NMOS transistor MN4 grounded.
本发明的放大器,工作原理是:所述自偏置负载放大器,在第三NMOS管MN3、第四NMOS管MN4之间构成了虚地点并为之提供栅极偏置电压,与此同时还提供增益并与共模电压调节电路复用负载的第二电阻R2、第三电阻R3;所述自适应电流偏置级利用第一放大器A1的虚短虚断特性将第一电阻R1的一端箝位到参考电压,当电源电压变化时,电源电压的变化量全部体现在第一电阻R1上,并相应转化为偏置电流变化量;鉴于放大器输入阻抗极大,该偏置电流全部流过第一NMOS管MN1。第一第二NMOS管MN1、MN2是电流镜镜像接法,故偏置电流最终也体现在第二NMOS管MN2上。共模电压调节电路中参考电流源被偏置电流抽拉后所剩余电流流经共模电压调节电路中负载电阻R2、R3形成自适应压降。如电源电压较高,则负载电阻R2、R3上压降较小,输出共模电压较高;如电源电压较低,则负载电阻R2、R3上压降较大,输出共模电压较低,从而实现了输出共模电压可调节的功能。The operating principle of the amplifier of the present invention is: the self-biased load amplifier forms a virtual point between the third NMOS transistor MN3 and the fourth NMOS transistor MN4 and provides a gate bias voltage for it, and at the same time provides Gain and multiplex the second resistor R2 and the third resistor R3 of the load with the common-mode voltage regulation circuit; the self-adaptive current bias stage clamps one end of the first resistor R1 to Reference voltage, when the power supply voltage changes, the variation of the power supply voltage is all reflected on the first resistor R1, and correspondingly converted into the variation of the bias current; in view of the extremely large input impedance of the amplifier, the bias current all flows through the first NMOS Tube MN1. The first and second NMOS transistors MN1 and MN2 are connected in a current mirror mirroring method, so the bias current is finally reflected on the second NMOS transistor MN2. The remaining current after the reference current source in the common-mode voltage regulation circuit is pulled by the bias current flows through the load resistors R2 and R3 in the common-mode voltage regulation circuit to form an adaptive voltage drop. If the power supply voltage is high, the voltage drop on the load resistors R2 and R3 is small, and the output common-mode voltage is high; if the power supply voltage is low, the voltage drop on the load resistors R2 and R3 is large, and the output common-mode voltage is low. Thus, the function of output common-mode voltage adjustable is realized.
该电路利用第一放大器A1将电阻第一电阻R1的一端固定在参考电位,当电源电压变小时,电阻上的压降降低,也就意味着流经电阻的电流减小。由于放大器的虚短虚断特性,该电流无法流过放大器输入端,故全部流经偏置第一NMOS管MN1,意味着镜像偏置第二NMOS管MN2从参考电流源抽取电流减少,放大器负载电阻R2、R3上有更多压降,从而实现低电源电压情况下输出共模电压更低,更易于与下级误差采样电路级联。The circuit uses the first amplifier A1 to fix one end of the first resistor R1 at the reference potential. When the power supply voltage becomes smaller, the voltage drop across the resistor decreases, which means that the current flowing through the resistor decreases. Due to the virtual short and virtual break characteristics of the amplifier, the current cannot flow through the input terminal of the amplifier, so it all flows through the biased first NMOS transistor MN1, which means that the mirror biased second NMOS transistor MN2 draws less current from the reference current source, and the amplifier load There are more voltage drops on the resistors R2 and R3, so that the output common-mode voltage is lower under the condition of low power supply voltage, and it is easier to cascade with the lower-level error sampling circuit.
如图2所示,为本实施例的低电压低功耗输出共模电压可调节放大器应用于可编程增益放大器中增益随温度变化的曲线图,其电源电压为700mv;从图中可以看出,在-40℃~80℃的温度范围内,单级运放增益变化量仅为0.1dB。As shown in Figure 2, it is a graph showing that the low-voltage, low-power output common-mode voltage adjustable amplifier of this embodiment is applied to a programmable gain amplifier as a function of temperature, and its power supply voltage is 700mv; it can be seen from the figure , in the temperature range of -40 ℃ ~ 80 ℃, the single-stage operational amplifier gain variation is only 0.1dB.
如图3所示,为本实施例的放大器应用于可编程增益放大器链增益随温度变化的曲线图,在700mv电源电压下,整个可编程增益放大器链路的增益变化量也仅为0.5dB多。As shown in Figure 3, it is a curve diagram of the gain of the amplifier in this embodiment applied to the programmable gain amplifier chain as a function of temperature. Under the power supply voltage of 700mv, the gain variation of the entire programmable gain amplifier chain is only more than 0.5dB. .
由上述可知,本发明的创新之处主要体现在自适应电流偏置级与共模电压调节上。本发明提出的输出共模电压可调节放大器,将电源电压的变化转化为偏置电流的变化,从而调节输出共模电压的大小,显著提高了低电压设计下后级电路尾电流源的漏源电压,提高电路的性能。故本发明适用于低电压低功耗下可编程增益放大器等应用场合。From the above, it can be seen that the innovation of the present invention is mainly embodied in the adaptive current bias stage and common-mode voltage regulation. The output common-mode voltage adjustable amplifier proposed by the present invention converts the change of the power supply voltage into the change of the bias current, thereby adjusting the size of the output common-mode voltage, and significantly improving the drain-source of the tail current source of the rear-stage circuit under low-voltage design voltage, improving the performance of the circuit. Therefore, the present invention is suitable for applications such as programmable gain amplifiers under low voltage and low power consumption.
上面结合附图对本发明的实施方式作了详细说明,但是本发明并不限于上述实施方式,在本领域普通技术人员所具备的知识范围内,还可以在不脱离本发明宗旨的前提下做出各种变化。The embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments, and can also be made without departing from the gist of the present invention within the scope of knowledge possessed by those of ordinary skill in the art. Variations.
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