Single-stage PFC converter post-stage active filter circuit

Abstract

The present invention designs a single-stage PFC converter rear-stage active filter circuit, which is composed of a single-stage PFC converter (1), a bidirectional converter (2), a bootstrap capacitor, a support capacitor and an output capacitor. The bidirectional converter (2) is a non-isolated DC bidirectional conversion circuit, which can adopt a synchronous buck or boost topology. The bidirectional converter (2) and the bootstrap capacitor and the support capacitor form a DC side active filter circuit: the support capacitor is connected to the rear end of the bidirectional converter (2), and the bootstrap capacitor is connected in series with the front end of the bidirectional converter (2) and then connected in parallel to the output end of the single-stage PFC converter (1). Advantages: 1. The bootstrap capacitor is used to divide the voltage, so that the working voltage of the bidirectional converter (2) is significantly reduced, and low-voltage power devices can be used. 2. The conversion power of the bidirectional converter (2) is much lower than the output power of the whole machine. 3. The efficiency of the whole machine is improved and the circuit cost is reduced. The present invention is a new technical solution for single-stage PFC+DC side active filtering, with a simple and ingenious topology, and can be widely used in various switching power supplies that require high input power factor and ripple-free output.

Description

Technical Field

[0001] The invention relates to a single-stage PFC converter post-stage active filtering circuit, which is a switching power supply technology and belongs to the technical field of power electronics. Background Art

[0002] At present, there are two types of technical solutions for high power factor isolated AC-DC converters, one is a single-stage conversion topology, and the other is a two-stage conversion topology.

[0003] The single-stage conversion topology mainly includes single-stage PFC (Power factor Correction) converters such as flyback and bridge, as well as combined single-stage converters consisting of PFC conversion and DC-DC conversion (sharing a set of switch tubes and control circuits). The single-stage PFC converter is characterized by a high power factor, but the DC output contains secondary harmonic ripple. The combined single-stage converter is characterized by a compromise optimization of the ripple at the DC output and the power factor at the AC input, which can reduce or eliminate the ripple at the DC output, but will reduce the power factor at the input.

[0004] The two-stage conversion topology solution is that the first stage is power factor correction AC-DC conversion, and the second stage is DC-DC conversion. There are two technical routes. One is that the first stage AC-DC is non-isolated, generally using the Boost topology; and the second stage DC-DC is isolated, mainly including topologies such as phase-shifted full-bridge, LLC conversion and single-ended conversion. The other is that the first stage AC-DC is isolated, that is, a single-stage PFC converter, mainly including topologies such as flyback and bridge; and the second stage DC-DC is non-isolated, mainly including topologies such as Buck, Boost, and Buck-Boost. The two-stage conversion topology can completely eliminate output ripple.

[0005] The main disadvantages of the two-stage conversion topology are: ① The circuit is complex. ② The overall efficiency is reduced. ③ The cost is high. These are all caused by the fact that all input electrical energy needs to go through two stages of power conversion before it can reach the load.

[0006] The above contents are only used to assist in understanding the technical solutions of the present invention, and do not constitute an admission that the above contents are all prior art. Summary of the invention

[0007] The purpose of the present invention is to overcome the deficiencies of the above-mentioned prior art and design a single-stage PFC converter post-stage active filter circuit. It is a new technical solution of single-stage PFC + DC side active filtering, which uses a simple and ingenious circuit topology to reduce the operating voltage and conversion power of the converter in the active filter circuit, improve the efficiency of the whole machine, and reduce the cost.

[0008] The technical solution of the present invention is as follows.

[0009] A single-stage PFC converter rear-stage active filter circuit is composed of a single-stage PFC converter (1), a bidirectional converter (2), a bootstrap capacitor (C1), a support capacitor (C2) and an output capacitor (Co). The single-stage PFC converter (1) adopts a flyback topology or a bridge topology and has one or more DC outputs; the bidirectional converter (2) is a non-isolated DC-DC bidirectional conversion circuit and adopts a synchronous buck topology or a synchronous boost topology or a synchronous boost-buck topology; the bidirectional converter (2) has a front end and a back end, and its four ports are respectively recorded as the front end positive P1, the front end negative N1 and the back end positive P2, and the back end negative N2; the so-called DC-DC bidirectional conversion is performed between the front end and the back end. Among them:

[0010] The positive pole Vo and the ground terminal GND of the DC output of the single-stage PFC converter (1) are respectively connected to the positive pole and the negative pole of the output capacitor (Co); the rear positive pole P2 and the rear negative pole N2 of the bidirectional converter (2) are respectively connected to the positive pole and the negative pole of the support capacitor (C2). The bidirectional converter (2) and the bootstrap capacitor (C1) and the support capacitor (C2) form a DC side active filter circuit, and there are two ways to connect the bidirectional converter (2) and the single-stage PFC converter (1): one is that the bidirectional converter (2) and the single-stage PFC converter (1) are connected to the same ground, that is, the positive pole Vo of the single-stage PFC converter (1) is connected to the positive pole of the bootstrap capacitor (C1), the negative pole of the bootstrap capacitor (C1) is connected to the front positive pole P1 of the bidirectional converter (2), and the front negative pole N1 of the bidirectional converter (2) is connected to the ground terminal GND of the single-stage PFC converter (1). The other is that the bidirectional converter (2) and the single-stage PFC converter (1) are connected to a common positive electrode, that is, the positive electrode Vo of the single-stage PFC converter (1) is connected to the front end positive P1 of the bidirectional converter (2), the front end negative N1 of the bidirectional converter (2) is connected to the positive electrode of the bootstrap capacitor (C1), and the negative electrode of the bootstrap capacitor (C1) is connected to the ground terminal GND of the single-stage PFC converter (1).

[0011] The so-called "bidirectional conversion circuit" refers to a circuit in which current / electric energy can flow in both directions, that is, current / electric energy can flow from the front end to the back end of the converter, and can also flow from the back end back to the front end.

[0012] Compared with the prior art, the present invention has the following advantages.

[0013] 1) The invention described above utilizes the bootstrap capacitor (C1) to divide the voltage, so that the front-end voltage (i.e., the voltage between the front-end positive P1 and the front-end negative N1) of the bidirectional converter (2) is significantly reduced, thereby significantly reducing the rear-end voltage (i.e., the voltage between the rear-end positive P2 and the rear-end negative N2). Therefore, the bidirectional converter (2) can use low-voltage power devices.

[0014] 2) In the invention, the reactive power processed by the bidirectional converter (2) is much lower than the AC component of the output power of the single-stage PFC converter (1). Therefore, the power loss of the bidirectional converter (2) is further reduced.

[0015] 3) The invention, by using a simple and ingenious circuit topology, reduces the operating voltage and conversion power of the bidirectional converter (2) in the subsequent active filter circuit, thereby improving the overall efficiency and reducing the circuit cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is the common ground connection schematic diagram of the post-stage active filter circuit of a single-stage PFC converter.

[0017] Figure 2 This is the common positive connection principle diagram of the post-stage active filter circuit of a single-stage PFC converter.

[0018] Among them, 1 is a single-stage PFC converter, 2 is a bidirectional converter, C1 is a bootstrap capacitor, C2 is a support capacitor, and Co is an output capacitor. u a —— AC input power, Vo —— positive pole, GND —— ground.

[0019] Figure 3 This is a common negative pole synchronous buck topology diagram that can be adopted by the bidirectional converter (2) of the invention.

[0020] Figure 4 This is a common positive synchronous buck topology diagram that can be used by the bidirectional converter (2) of the invention.

[0021] Among them, Q1, Q2 are switching tubes, and Lr is the filter inductor. DETAILED DESCRIPTION

[0022] The present invention will be described and analyzed in detail below with reference to the accompanying drawings and preferred embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention and not all of them.

[0023] It should be further explained that the descriptions such as "front end" and "back end" of the bidirectional converter (2) involved in the present invention are only used for the purpose of convenient indicative description and should not be understood as indicating its specific location or proper noun.

[0024] 1. Preferred embodiments of the present invention

[0025] like Figure 1 , Figure 2As shown, the post-stage active filter circuit of a single-stage PFC converter is composed of a single-stage PFC converter (1), a bidirectional converter (2), a bootstrap capacitor (C1), a support capacitor (C2) and an output capacitor (Co). The single-stage PFC converter (1) adopts a flyback topology or a bridge topology and has one or more DC outputs. The bidirectional converter (2) is a non-isolated DC-DC bidirectional conversion circuit, which adopts a synchronous buck topology or a synchronous boost topology or a synchronous boost-buck topology; the bidirectional converter (2) has a front end and a back end, and its four ports are respectively recorded as the front end positive P1, the front end negative N1 and the back end positive P2, and the back end negative N2; the so-called DC-DC bidirectional conversion is performed between the front end and the back end. Among them:

[0026] The positive pole Vo and the ground terminal GND of the DC output of the single-stage PFC converter (1) are respectively connected to the positive pole and the negative pole of the output capacitor (Co); the rear positive P2 and the rear negative N2 of the bidirectional converter (2) are respectively connected to the positive pole and the negative pole of the support capacitor (C2). The bidirectional converter (2) and the bootstrap capacitor (C1) and the support capacitor (C2) form a DC side active filter circuit, and there are two ways to connect it with the single-stage PFC converter (1). One is that the bidirectional converter (2) and the single-stage PFC converter (1) are connected to the same ground, such as Figure 1 As shown; that is, the positive electrode Vo of the single-stage PFC converter (1) is connected to the positive electrode of the bootstrap capacitor (C1), the negative electrode of the bootstrap capacitor (C1) is connected to the front end positive P1 of the bidirectional converter (2), and the front end negative N1 of the bidirectional converter (2) is connected to the ground terminal GND of the single-stage PFC converter (1). Another is that the bidirectional converter (2) and the single-stage PFC converter (1) are connected with a common positive electrode, as shown in FIG. Figure 2 As shown; that is, the positive electrode Vo of the single-stage PFC converter (1) is connected to the front end positive P1 of the bidirectional converter (2), the front end negative N1 of the bidirectional converter (2) is connected to the positive electrode of the bootstrap capacitor (C1), and the negative electrode of the bootstrap capacitor (C1) is connected to the ground GND of the single-stage PFC converter (1).

[0027] The load is connected by the positive electrode Vo and the ground terminal GND.

[0028] The so-called "bidirectional conversion circuit" refers to a circuit in which current / electric energy can flow in both directions, that is, current / electric energy can flow from the front end to the back end of the converter, or from the back end back to the front end. For the bidirectional converter (2), a synchronous buck topology, a synchronous boost topology, or a synchronous boost-buck topology can be used, all of which can achieve bidirectional flow of current / electric energy.

[0029] like Figure 3As shown, the bidirectional converter (2) adopts a common negative synchronous buck topology and is composed of two switch tubes (Q1, Q2) and a filter inductor (Lr). The front negative N1 and the rear negative N2 are connected, the source of the switch tube (Q2) is connected to the front negative N1 and the rear negative N2; the drain of the switch tube (Q2) is connected to the source of the switch tube (Q1) and one end of the filter inductor (Lr), and the other end of the filter inductor (Lr) is connected to the front positive P1; the drain of the switch tube (Q1) is connected to the rear positive P2.

[0030] like Figure 4 As shown, the bidirectional converter (2) adopts a common positive synchronous buck topology and is composed of two switch tubes (Q1, Q2) and a filter inductor (Lr). The front positive P1 and the rear positive P2 are connected, the drain of the switch tube (Q1) is connected to the front positive P1 and the rear positive P2; the source of the switch tube (Q1) is connected to the drain of the switch tube (Q2) and one end of the filter inductor (Lr), and the other end of the filter inductor (Lr) is connected to the front negative N1; the source of the switch tube (Q2) is connected to the rear negative N2.

[0031] 2. Working Principle of the Invention

[0032] The working principle of the post-stage active filter circuit of the single-stage PFC converter is analyzed in detail from the following four aspects. These four aspects can be summarized as: the output voltage of the single-stage PFC converter; the voltage transfer function of the bidirectional converter (2); reactive power distribution and overall efficiency analysis; the working voltage and capacitor selection of the bidirectional converter (2).

[0033] 2.1 Output voltage of single-stage PFC converter (1)

[0034] The so-called single-stage PFC (Power Factor Correction) converter refers to a power conversion circuit that outputs a DC voltage and implements power factor correction through a single-stage power conversion. Its output is a DC voltage V O and DC current I O , the input quantity is AC voltage u a and AC current i a The control strategy of the converter is to stabilize the required DC output while achieving power factor correction at the input.

[0035] The so-called power factor correction (PFC) is the alternating current i a Tracking AC Voltage u a , so that their waveforms are consistent and their phases are the same, thus achieving a high power factor. Theoretically, the power factor PF≤1. When PF=1, there is:

[0036]

[0037] In formula (E-1), V a For AC voltage u a The effective value of I a For AC current i a The effective value of ω is the angular frequency of the sinusoidal alternating current. Assume that the efficiency of the single-stage PFC converter is η , then the AC input power of the single-stage PFC converter is P a and DC output power P o They are:

[0038]

[0039] The output power P o Decomposition into DC components Plus AC In the form of:

[0040]

[0041] Similarly, the DC output voltage V O , which can be decomposed into the DC component Plus AC of the form, namely:

[0042]

[0043] Taking the resistive load as an example, the following analyzes the AC component in the DC output voltage Because the load containing reactance components (inductive reactance or capacitive reactance) is connected in parallel with the filter capacitor, it can be equivalent to a parallel model of capacitor and resistor.

[0044] According to the law of conservation of energy, linear superposition theorem and circuit theory, the following differential equation is obtained:

[0045]

[0046] in, C is the filter capacitor, R o is the load resistance. Considering the actual , formula (E-5) is simplified to:

[0047]

[0048] Solving the differential equation of formula (E-6), we can obtain the AC component The expression is as follows:

[0049]

[0050] It can be seen from formula (E-7) that the AC component of the output voltage of the single-stage PFC converter is The angular frequency is twice the angular frequency of the input AC voltage, so it is called the second harmonic. Increase the filter capacitor C The second harmonic can be reduced, but it cannot be completely eliminated. If you want to completely eliminate the second harmonic, you need to use other technical means.

[0051] 2.2 Voltage transfer function of bidirectional converter (2)

[0052] There are six basic topologies for non-isolated DC-DC bidirectional conversion circuits, namely synchronous Buck, Boost, Buck-Boost, Sepic, Cuk, and Zeta. Buck is a step-down conversion, Boost is a step-up conversion, and Buck-Boost, Sepic, Cuk, and Zeta are step-up-down conversions. When the non-isolated DC-DC bidirectional conversion circuit operates in the current continuous mode, its voltage transfer function is:

[0053]

[0054] In formula (E-8), D is the on-duty cycle of the switch tube, that is, the duty cycle of PWM control; V 1 and V 2 are the front-end voltage and the back-end voltage of the non-isolated DC-DC bidirectional conversion circuit respectively.

[0055] The bidirectional converter (2) in the invention can adopt one of the six basic topologies mentioned above. Figure 1 and Figure 3 , taking the bidirectional converter (2) adopting the common cathode synchronous buck topology and being connected to the single-stage PFC converter (1) as an example, a detailed analysis is carried out.

[0056] Assume the voltage of the bootstrap capacitor (C1) V C1 and the voltage of the support capacitor (C2) V C2 They are:

[0057]

[0058] In formula (E-9), and are the DC and AC components of the bootstrap capacitor (C1) voltage respectively; and They are the DC component and AC component of the support capacitor (C2) voltage respectively.

[0059] like Figure 1 and Figure 3 As shown, the front-end voltage of the bidirectional converter (2) V 1 and rear voltage V 2 are:

[0060]

[0061] According to equation (E-8), if the bidirectional converter (2) operates in the current continuous mode, its voltage transfer function is:

[0062]

[0063] In formula (E-11), D t is the on-duty ratio of the switch tube Q1, which changes with time. Ignoring the dead time, the on-duty ratio of the switch tube Q2 is (1- D t ). If , then the output voltage and V C1 , V C2 The relationship is:

[0064]

[0065] Obviously, if we want to completely eliminate V The second harmonic in the Dt In this case, the AC component (i.e., reactive power) of the output power of the single-stage PFC converter (1) is completely absorbed by the bootstrap capacitor (C1) and the support capacitor (C2), so and It is a second harmonic form similar to formula (E-7).

[0066] 2.3 Reactive power distribution and overall efficiency analysis

[0067] The bidirectional converter (2) together with the bootstrap capacitor (C1) and the support capacitor (C2) form a DC side active filter circuit. When the DC output voltage is completely filtered out, V o When the second harmonic is generated, there is only a DC component in the output voltage. According to equation (E-3), the AC component of the output current of the single-stage PFC converter (1) is for:

[0068]

[0069] because , then the AC component of the bootstrap capacitor C1 voltage for:

[0070]

[0071] Without loss of generality, for ease of description, the following parameters can be set:

[0072]

[0073] In formula (E-15), λ is called the bootstrap coefficient, δ It is called the ripple factor; usually λ =0.7~0.9.

[0074] According to equations (E-9), (E-13) and (E-15), the reactive power absorbed by the bootstrap capacitor C1 is for:

[0075]

[0076] According to equation (E-16) and equation (E-3), the reactive power absorbed by the supporting capacitor C2 is for:

[0077]

[0078] According to equation (E-17) and equation (E-7), the AC component of the voltage of the supporting capacitor C2 is obtained: for:

[0079]

[0080] From equations (E-16) and (E-17), it can be seen that the AC reactive power and It contains not only second harmonics but also higher harmonics, wherein the higher harmonics are caused by active filtering performed by the bidirectional converter (2).

[0081] The AC power processed by the bidirectional converter (2) is , in theory is reactive power. However, the AC power flowing into and out of the supporting capacitor C2 through the bidirectional converter (2) is lossy, and this loss is compensated by active power to maintain V C1 and V C2 This loss is denoted as Δ P2, Δ P 2 includes the losses of the switch tubes (Q1, Q2), the filter inductor Lr and the support capacitor C2. According to formula (E-17), the average value of the loss can be obtained by integration: for:

[0082]

[0083] In the formula, η 2 is the conversion efficiency of the bidirectional converter (2). It can be seen from formula (E-19) that the AC power output of the single-stage PFC converter (1) Among them, only (1-λ) That is, only a small part of the filter loss is generated, and the overall efficiency is greatly improved. The larger the λ, the smaller the loss. Therefore, the DC voltage component of the bootstrap capacitor C1 should be increased as much as possible. .

[0084] 2.4 Operating voltage and capacitor selection for bidirectional converter (2)

[0085] According to equations (E-14) and (E-18), the magnitude of the AC component of the voltage of the bootstrap capacitor C1 and the support capacitor C2 is:

[0086]

[0087] According to formula (E-11), since 0≤ D t ≤1, so a necessary condition for the normal operation of the bidirectional converter (2) is:

[0088]

[0089] Substituting equation (E-9) and equation (E-15) into equation (E-21), we obtain:

[0090]

[0091] Without loss of generality, we can choose:

[0092]

[0093] According to formula (E-20) and formula (E-15), it can be deduced that:

[0094]

[0095] An initial state that needs to be considered is that when the single-stage PFC converter (1) is already running and the bidirectional converter (2) is not yet running, the body diode of the switch tube Q1 is turned on, and the bootstrap capacitor C1 and the support capacitor C2 will output the voltage V oVoltage division. In order to ensure that the voltage on C2 is not higher than the voltage when it is in stable operation, and the voltage on C1 is not lower than the voltage when it is in stable operation, the support capacitor C2 is selected as follows:

[0096]

[0097] It should be noted that since the bootstrap capacitor C1 and the support capacitor C2 completely absorb the second harmonic output by the single-stage PFC converter (1), the capacity of the output capacitor Co can be much smaller than that of the bootstrap capacitor C1 and the support capacitor C2. This is why it is called "output capacitor" instead of "filter capacitor".

[0098] According to formula (E-25) and formula (E-20), we can get σ for:

[0099]

[0100] Substitute equation (E-26) into the first equation of equation (E-23) and solve:

[0101]

[0102] According to formula (E-10), the front-end voltage of the bidirectional converter (2) V 1 and rear voltage V The peak values ​​of 2 are:

[0103]

[0104] In the formula, and They are V 1 and V 2. It can be seen from formula (E-28) that as the bootstrap coefficient λ increases, the peak values ​​of the front-end voltage and the rear-end voltage of the bidirectional converter (2) and are reduced and are much smaller than the output DC voltage , that is, the operating voltage of the bidirectional converter (2) is significantly reduced. Therefore, the bidirectional converter (2) can select low-voltage power devices with low on-resistance, thereby further improving efficiency and reducing costs.

[0105] So far, the bidirectional converter (2) adopts a common negative electrode synchronous buck topology and is connected to a common ground with the single-stage PFC converter (1) as a typical embodiment, and its working principle is analyzed in detail. When the bidirectional converter (2) adopts a non-isolated DC-DC bidirectional conversion circuit other than the synchronous buck topology, and is connected to a common positive electrode of the output voltage with the single-stage PFC converter (1), the analysis process can be carried out according to similar principles and will not be described in detail here.

[0106] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification and drawings under the inventive concept of the present invention, or directly or indirectly applied in other related technical fields, are included in the patent protection scope of the present invention.

Claims

1. A single-stage PFC converter rear-stage active filter circuit, comprising a single-stage PFC converter (1), a bidirectional converter (2), a bootstrap capacitor C1, a support capacitor C2 and an output capacitor Co; the single-stage PFC converter (1) adopts a flyback topology or a bridge topology, and has one or more DC outputs; the bidirectional converter (2) is a non-isolated DC-DC bidirectional conversion circuit, and adopts a synchronous buck topology or a synchronous boost topology or a synchronous boost-buck topology; the bidirectional converter (2) has a front end and a rear end, and its four ports are respectively recorded as a front end positive P1, a front end negative N1 and a rear end positive P2, and a rear end negative N2; the so-called DC-DC bidirectional conversion is performed between the front end and the rear end; and its characteristics are: The positive electrode Vo and the ground terminal GND of the DC output of the single-stage PFC converter (1) are respectively connected to the positive electrode and the negative electrode of the output capacitor Co, and the rear end positive P2 and the rear end negative N2 of the bidirectional converter (2) are respectively connected to the positive electrode and the negative electrode of the support capacitor C2; the bidirectional converter (2) and the bootstrap capacitor C1 and the support capacitor C2 form a DC side active filter circuit, and there are two ways to connect the bidirectional converter (2) and the single-stage PFC converter (1): one is that the bidirectional converter (2) and the single-stage PFC converter (1) are connected to the same ground, that is, the positive electrode Vo of the single-stage PFC converter (1) is connected to the bootstrap capacitor C1; the other is that the positive electrode Vo of the single-stage PFC converter (1) is connected to the bootstrap capacitor C1; The positive electrode of the capacitor C1 and the negative electrode of the bootstrap capacitor C1 are connected to the positive front end P1 of the bidirectional converter (2), and the negative front end N1 of the bidirectional converter (2) is connected to the ground end GND of the single-stage PFC converter (1); the other is that the bidirectional converter (2) and the single-stage PFC converter (1) share a common positive electrode, that is, the positive electrode Vo of the single-stage PFC converter (1) is connected to the positive front end P1 of the bidirectional converter (2), the negative front end N1 of the bidirectional converter (2) is connected to the positive electrode of the bootstrap capacitor C1, and the negative electrode of the bootstrap capacitor C1 is connected to the ground end GND of the single-stage PFC converter (1).

2. The single-stage PFC converter post-stage active filter circuit according to claim 1, characterized in that: The bidirectional converter (2) adopts a common negative synchronous buck topology and is composed of two switch tubes Q1 and Q2 and a filter inductor Lr; the front end negative N1 and the rear end negative N2 are connected, the source of the switch tube Q2 is connected to the front end negative N1 and the rear end negative N2; the drain of the switch tube Q2 is connected to the source of the switch tube Q1 and one end of the filter inductor Lr, and the other end of the filter inductor Lr is connected to the front end positive P1; the drain of the switch tube Q1 is connected to the rear end positive P2.

3. The single-stage PFC converter post-stage active filter circuit according to claim 1, characterized in that: The bidirectional converter (2) adopts a common positive synchronous buck topology and is composed of two switch tubes Q1, Q2 and a filter inductor Lr; the front end positive P1 and the rear end positive P2 are connected, the drain of the switch tube Q1 is connected to the front end positive P1 and the rear end positive P2; the source of the switch tube Q1 is connected to the drain of the switch tube Q2 and one end of the filter inductor Lr, and the other end of the filter inductor Lr is connected to the front end negative N1; the source of the switch tube Q2 is connected to the rear end negative N2.

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