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A novel internal compensation technique named dual frequency compensation is proposed to improve the stability and the transient response of the onchip output capacitor three stage lowdropout linear voltage regulator (LDO). It exploits a combination of amplification and differentiation to sufficiently separate the dominant pole from the first nondominant pole so that the latter is located after the unity gain frequency regardless of the load current value. The proposed LDO regulator is analyzed, designed, and simulated in standard 0.18 µm low voltage CMOS technology. The presented LDO regulator delivers a stable voltage of 1.2 V for an input supply voltage range of 1.351.85 V with a maximum line deviation of 4.68mV/V and can supply up to 150mA of the load current. The maximum transient variation of the output voltage is 54.5 mV when the load current pulses from 150mA to 0mA during a fall time of 1µs. The proposed LDO regulator has a low figure of merit compared with recent LDO regulators.
power management, system on a chip (SoC), LowDropOut regulator (LDO), stability, minimum load current, transient load regulation, CMOS technology
Many systemonachip (SoC) applications integrate circuit blocks, such as digital, analog and radiofrequency blocks [14]. Charge pump regulators are commonly used to generate high voltages for lighting or memory units [5, 6]; switching converters are employed to regulate digital blocks, due to their high power efficiency [7, 8]; and lowdropout linear voltage regulators are used to provide low noise supply voltage with very low ripple for noise sensitive blocks, such as analog/RF circuits [9, 10]. An example that highlights the presentday importance of voltage regulators and power management blocks can be found in ref. [11], where the power supply requirements for a CodeDivision Multiple Access (CDMA) modem of a mobile phone are described. As shown in Figure 1, LDO regulators play a very important role in the integrated power management unit in modern portable electronic devices [11], they scales down the supply voltage to provide for many various other blocks.
An important issue in LDO voltage regulator design is stability, which has a direct impact on the transient response of this system. In addition, the downscaling of the supply voltage and the decrease of the intrinsic gain of the MOS transistor for nanometric CMOS technologies [12, 13] requires the use of multiple stages in the implementation of the LDO regulator, this degrades the closeloop response by the presence of multiple poles, hence the need to develop a robust compensation method. Compensation can be external or internal. Generally, external compensation is achieved with a high value capacitor in the order of µF [14]. As for internal compensation, Miller compensation is one of the most widely used techniques [10], but other techniques and approaches can be found in literature [1528].
Figure 1. Power management unit in modern portable devices [11]
In this work a novel frequency compensation technique is proposed to achieve the stability for wide range of the load current for the LDO regulator and also enhance his transient response. In section 2, a literature review of stability enhancement is summarized. In section 3, the proposed LDO regulator circuit is given and detailed analysis is performed. In section 4, the simulation results are given to show the performance of the proposed LDO regulator in terms of stability, transient response and others parameters accompanied by a comparison with previous related works. Finally, in section 5, the simulation results are given to show the performance of the proposed LDO regulator in terms of stability, transient response and others parameters accompanied by a comparison with previous related works.
Many solutions have been proposed in the literature to improve the stability of LDO regulators with small current load values. One of the earliest proposals [15] uses a compensation block to control the damping factor [16]. This improves the stability of the system and increases the bandwidth. A variant of this work can be found in [17], where a block is introduced to control the quality factor of the pair of nondominant complex poles. To save power, the active load of the differential pair of the error amplifier is reused as a current buffer. An additional branch is included to introduce a zero in the negative real halfplane with the twofold objective of improving the stability and increasing the maximum current at the gate of pass transistor. Unfortunately, every stage of the control circuit is loaded by compensating capacitors, which causes a decrease in the SlewRate (SR) of the LDO regulator. Capacitive multipliers were also used in [1822]. As an example, in [18], a differentiator, formed by a capacitor and a current buffer, is introduced. This buffer serves a double purpose. First of all, it introduces a fast path between the output of the LDO regulator and the gate of pass transistor. Second, the buffer helps to separate the poles, since the capacitor appears at the gate of pass transistor multiplied by the gain of the current buffer. It is worth noting that the use of a current buffer is compatible with other compensation techniques. As an example, in [22], a current buffer is used as part of a classical Reverse Nested Miller Compensation (RNMC). In [23], adaptive power transistors technique is proposed to allow the LDO regulator to transform itself between two stage and three stage cascaded topologies with respective power transistor, depending on the load current condition. This later technique achieves high stability and good transient response. Most of these techniques and approaches suffer from the instability problem at very low load current, while several applications need the LDO regulator to hold the output and provide good performance under a noload current condition such as CMOS RAM keepalive applications.
To overcome the limitations of the classical internal compensation, an alternative topology called Flipped Voltage Follower (FVF) has been proposed [24]. This method has been well analyzed, developed and applied to the LDO regulator [25], it is characterized by a local feedback which makes it possible to achieve a low output impedance, and consequently to improve the SR at the gate of pass transistor, which improves the transient response as well as the stability, but because of the low value of the static gain generated by this method [25], the performance of the line and load regulations remains limited which degrades the transient response. To improve the performance of stability and regulation, several LDO regulators have been proposed, such as the one that uses the Cascode Flipped Voltage Follower [26], the multipleloop LDO regulator based on the flipped voltage follower [27] and the LDO regulator with mixed internal compensation which marries the Miller compensation and the flipped voltage follower [28].
3.1 Main blocks of proposed LDO regulator
The diagram block of proposed LDO regulator is shown in Figure 2, while Figure 3 gives transistor implementation of proposed error amplifier (EA). For error amplifier design, a singleended twostage error amplifier with fully differential input is chosen [29], it consists of M_{1}M_{6} transistors, bias current I_{B,EA }and common feedback resistor R_{CM}. A fullydifferential PMOS M_{1} input stage is used to achieve high power supply noise rejection. The third stage is composed by the PMOS pass transistor M_{P} to achieve low dropout voltage [10]. The feedback network is composed by the resistors R_{FB1} and R_{FB2}. R_{L} is the load resistor which models the low voltage systemonchip powered by the LDO regulator output. The load capacitor C_{L} is integrated on chip, which is essential to improve the transient response. V_{I} is the power supply input voltage, V_{REF} is the reference voltage provided by another subcircuit, V_{G,P }represent the voltage at the gate of pass transistor M_{P}. V_{O} is the output voltage of LDO regulator. The compensation network will be clarified later in this section.
Figure 2. Block diagram of the proposed LDO regulator
Figure 3. Proposed error amplifier (EA)
3.2 Stability analysis
3.2.1 Uncompensated frequency response
To determine the uncompensated openloop transfer function, of the proposed LDO regulator system, defined by Eq. (1), a small signal model is established and it is represented in Figure 4. By applying the Kirchhoff current laws, we obtain the transfer function H_{ol,u}(s) given by Eq. (2). Where, H_{0,u }is the DC gain given by Eq. (3), where β is the feedback factor expressed by Eq. (4). g_{m1} is the transconductance of the EA first stage which is equal to that of transistor M_{1} and R_{O1,EA }represents the output resistance of the EA first stage expressed by Eq. (5), where r_{o1} and r_{o2} represent the small output resistances of transistors M_{1} and M_{2}, respectively. g_{m3} and g_{m,P }represent the transconductance of EA second stage, which is equal to that of transistor M_{3}, and the transconductance of pass transistor M_{P}, respectively. r_{o6} is the small signal output resistance of EA second stage which is equal to small signal output resistance of transistor M_{6}. R_{O} is the output resistance of LDO regulator given by Eq. (6), where r_{o,P }is the output resistance of M_{P}. Note that s denotes the complex variable of Laplace.
Figure 4. Small signal model of the proposed uncompensated LDO
${{H}_{ol,u}}(s)=\frac{{{v}_{fb}}}{{{v}_{ref}}}$ (1)
${{H}_{ol,u}}(s)=\frac{{{H}_{0,u}}(1+\frac{s}{{{z}_{RHP}}})}{(1\frac{s}{{{p}_{d}}})(1\frac{s}{{{p}_{nd}}})(1\frac{s}{{{p}_{3}}})}$ (2)
${{H}_{0,u}}=\beta {{g}_{m1}}{{g}_{m3}}{{g}_{m,P}}{{R}_{O1,EA}}\quad{{r}_{o6}}{{R}_{O}}$ (3)
$\beta =\frac{{{R}_{FB2}}}{{{R}_{FB1}}+{{R}_{FB2}}}$ (4)
${{R}_{O1,EA}}={{r}_{o1}}//{{r}_{o2}}//{{R}_{CMFB}}$ (5)
${{R}_{O}}={{r}_{o,P}}//({{R}_{FB1}}+{{R}_{FB2}})//{{R}_{L}}$ (6)
The transfer function contains a right halfplane (RHP) zero z_{RHP} given by Eq. (7), where C_{gd,P }is the parasitic draintosource capacitance. The frequency location of z_{RHP} changes with load current I_{L} (or value of R_{L}), because g_{m,P }and C_{gd,P} change with I_{L} and this is due to the fact that M_{p} changes the region of operation according to the variation range of I_{L} [9].
${{z}_{RHP}}=\frac{{{g}_{m,P}}}{{{C}_{gd,P}}}$ (7)
According to Eq. (2), the transfer function contains three left halfplane (LHP) poles p_{d}, p_{nd} and p_{3}, where their locations change relatively with the load current. The dominant pole p_{d} is located at the gate node of M_{P} (v_{g,P }voltage in Figure 4) due to the large value of C_{G,P }and r_{o6}, where C_{G,P} represents the total capacitance connected between the M_{P} gate and the small signal ground. The nondominant pole p_{nd} is located at the output node (v_{o} voltage in Figure 4). The third pole p_{3} represents the high frequency pole and it’s located at the first stage output node of EA (v_{1} voltage in Figure 4). This last pole is independent of the load current and therefore does not affect the stability. For the proposed LDO regulator design, M_{p} operates in subthreshold region when the load current is at its minimum value I_{L,min}, while it operates in the saturation region at the maximum value I_{L,max} of load current. In this case the approximate expressions of these three poles are given by:
${{p}_{d}}\approx \frac{1}{{{r}_{o6}}\quad({{g}_{m,P}}\quad{{R}_{O}}{{C}_{gd,P}}\quad+{{C}_{G,P}}\quad)+{{R}_{O}}{{C}_{O}}}$ (8)
${{p}_{nd}}\approx \frac{{{r}_{o6}}\quad({{g}_{m,P}}\quad{{R}_{O}}{{C}_{gd,P}}+{{C}_{G,P}})\quad+{{R}_{O}}{{C}_{O}}}{{{R}_{o6}}\quad{{R}_{O}}({{C}_{gd,P}}\quad+{{C}_{G,P}}\quad){{C}_{O}}}$ (9)
${{p}_{3}}\approx \frac{1}{{{R}_{O1,EA}}\quad{{C}_{O1,EA}}}$ (10)
where, C_{G,P}=C_{O2,EA}+C_{gd,P} and C_{O}=C_{L}+C_{db,P}. C_{O1,EA }and C_{O2,EA }represent the output capacitances of EA first stage and EA second stage, respectively. C_{gd,P}, C_{gs,P} and C_{db,P} represent the parasitic capacitances gatetodrain, gatetosource and draintobulk of the pass transistor M_{P}.
(a) Bode plan location
(b) complex s plan location
Figure 5. Polezero location with load current variation
Figure 5 shows the dependence of zeros and poles location on the load current I_{L} in the Bode plan and in the complex s plane, respectively. The frequency location is presented in term of angular frequency ω, where ω_{zRHP}=z_{RHP}, ω_{pd}=−ω_{pd}, ω_{pnd}=−p_{nd }and ω_{3}=−p_{3}. For low I_{L}, the RHP zero is located in the middle frequencies, which introduces a phase shift of −90°, this pushes the nondominant pole towards the low frequencies, before the unity gain angular frequency ω_{UGF}. Therefore the magnitude curve in the Bode diagram intersects the frequency axis by a slope of −40 dB/decade and consequently the LDO regulator is unstable. For a case of the large load current, the RHP zero is pushed in the high frequencies, the nondominant pole is located after the unity gain frequency, so the phase margin is positive but insufficient (less than 45°) to stabilize closed loop response of the LDO regulator system.
It is clear that to stabilize the LDO regulator, it is necessary to separate the dominant and nondominant poles while keeping a phase margin greater than 45 degree for the entire load current range required by the specifications and keeping higher the unity gain frequency to have a fast transient response, this is achieved by adding a LHP zeros well placed with respect to the nondominant pole and unity gain frequency locations.
3.2.2 Compensated frequency response
To stabilize the proposed three stage LDO regulator, a dual compensation circuit has been inserted between the LDO output and the pass transistor gate. The compensation network is given by Figure 6. It is composed of two differentiatorcurrent amplifier blocks, (C_{C1}, R_{C1}, M_{7}, M_{8}) and (C_{C2}, R_{C2}, M_{9}, M_{10}), whose role is to separate the dominant pole from the first nondominant pole and to create LHP zeros to increase the phase margin. The proposed compensation block has no effect on the elimination of the RHP zero. The compensation circuit requires a symmetrical bias current I_{B,C}. The cascode trasistors M_{7c}, M_{8c} and M_{13c} help to minimize the effect of channel length modulation to improve matching performance.
Figure 6. Transistor MOS implementation of proposed frequency compensation circuit
Figure 7. Small signal model of LDO regulator with proposed compensation circuit
To determine the open loop transfer function H_{ol,c}(s) of the compensated system, the smallsignal equivalent model was made as shown in Figure 7. By application of Kirchhoff's current law and after some mathematical manipulations and some justified simplifications, we find that H_{ol,c}(s) can be expressed as:
$\begin{align} & {{H}_{ol,c}}(s)\approx \frac{{{H}_{0,c}}.(1+\frac{s}{{{z}_{RHP}}})(1\frac{s}{{{z}_{1}}})(1\frac{s}{{{z}_{2}}})}{(1\frac{s}{{{p}_{d}}})(1+\frac{{{a}_{2}}}{{{a}_{1}}}s+\frac{{{a}_{3}}}{{{a}_{1}}}{{s}^{2}})(1+\frac{{{a}_{4}}}{{{a}_{3}}}s)(1\frac{s}{{{p}_{5}}})} \\ \end{align}$ (11)
where,
${{H}_{0,c}}=\beta {{g}_{m1}}{{g}_{m3}}{{g}_{m,P}}{{R}_{O1,EA}}{{R}_{G,P}}{{R}_{O}}$ (12)
${{R}_{G,P}}={{r}_{o6}}//{{r}_{o10}}//({{g}_{m8}}r_{o8}^{2})$ (13)
${{z}_{1}}\approx \frac{1}{{{R}_{C}}{{C}_{C}}}$ (14)
${{z}_{2}}\approx \frac{4}{{{R}_{C}}{{C}_{C}}}$ (15)
${{p}_{d}}\approx \frac{4}{{{R}_{G,P}}\quad{{g}_{m,P}}\quad{{R}_{O}}[({{g}_{m10}}\quad+{{g}_{m8}}\quad){{R}_{C}}{{C}_{C}}+{{C}_{gd,P}}\quad]}$ (16)
${{a}_{1}}\approx \frac{{{R}_{G,P}}\quad{{g}_{m,P}}\quad{{R}_{O}}[({{g}_{m10}}\quad+{{g}_{m8}}\quad){{R}_{C}}{{C}_{C}}+{{C}_{gd,P}}\quad]}{4}$ (17)
$\begin{align} & {{a}_{2}}\approx \frac{R_{C}^{2}C_{C}^{2}}{4}+{{R}_{G,P}}{{C}_{G,P}}{{R}_{O}}({{C}_{O}}+{{C}_{C,tot}}+{{C}_{gd,P}}) +\frac{{{R}_{C}}{{C}_{C}}}{2}[{{R}_{G,P}}{{C}_{G,P}}+{{R}_{O}}({{C}_{O}}+{{C}_{C,tot}}+{{C}_{gd,P}})] \\ \end{align}$ (18)
$\begin{align} & {{a}_{3}}\approx \frac{R_{C}^{2}C_{C}^{2}}{4}[{{R}_{G,P}}{{C}_{G,P}}+{{R}_{O}}({{C}_{O}}+{{C}_{C,tot}}+{{C}_{gd,P}})]\mathop{{}}_{{}}^{{}}+{{R}_{G,P}}{{C}_{G,P}}{{R}_{O}}({{C}_{O}}+{{C}_{C,tot}}+{{C}_{gd,P}})\frac{{{R}_{C}}{{C}_{C}}}{2} \\ \end{align}$ (19)
$\begin{align} & {{a}_{4}}\approx \frac{R_{C}^{2}C_{C}^{2}}{4}(\frac{{{C}_{i1}}}{{{g}_{m7}}}+\frac{{{C}_{i2}}}{{{g}_{m9}}}){{R}_{G,P}}{{C}_{G,P}}+\frac{R_{C}^{2}C_{C}^{2}}{4}(\frac{{{C}_{i1}}}{{{g}_{m7}}}+\frac{{{C}_{i2}}}{{{g}_{m9}}}){{R}_{O}}({{C}_{O}}+{{C}_{C,tot}}+{{C}_{gd,P}})] +\frac{R_{C}^{2}C_{C}^{2}}{4}{{R}_{G,P}}{{C}_{G,P}}{{R}_{O}}({{C}_{O}}+{{C}_{C,tot}}+{{C}_{gd,P}}) \\ \end{align}$ (20)
${{p}_{5}}\approx \frac{1}{{{R}_{O1,EA}}\quad{{C}_{O1,EA}}}$ (21)
H_{0,c} represents the DC gain of compensated LDO whose value is very close to the value of H_{0,u }previously expressed by Eq. (3). R_{G,P }is the total equivalent resistance connected between the gate node of M_{p} and ground. It also includes the output resistances of the two current amplifiers of the compensation circuit as shown by its expression given by Eq. (13). In the term a_{1}, gm_{8} and gm_{10} represent the transconductances of the amplifying transistors M_{8} and M_{10} of the compensation circuit, respectively. In the term a_{4}, g_{m7} and C_{i1} represent the transconductance of M_{7} and the equivalent input capacitor of differentiatorcurrent amplifier (C_{C1}, R_{C1}, M_{7}, M_{8}) in compensation circuit. Likewise, g_{m9} and C_{i2} represent the transconductance of M_{9} and the equivalent input capacitor of differentiatorcurrent amplifier (C_{C2}, R_{C2}, M_{9}, M_{10}).
The dominant pole p_{d} is located at the gate of M_{P}. z_{1} and z_{2} are the LHP zeros created by the compensation circuit, where RC represent the compensation resistance such as R_{C1}=R_{C2}=RC and C_{C} is the compensation capacitance such as C_{C1}=C_{C2}=C_{C}. The analysis shows that the nondominant pole corresponds to two complex conjugate poles which are the roots of the polynomial equation presented in the denominator of Eq. (11). The two complex conjugate poles p_{2} and p_{3} are given by Eq. (22), where ω_{0} is the corner angular frequency given by Eq. (23) and ζ represents the damping factor expressed by Eq. (24). When I_{L} continues to increase, the quality factor Q=1/(2ζ) increases, and the resonance phenomenon appears in the vicinity of the angular frequency ω_{0}, whose resonant angular frequency, noted ω_{r}, is expressed by Eq. (25). The fourth pole is given by p_{4}=−(a_{3}/a_{4}), while the fifth pole p_{5} is located at the output node of the error amplifier first stage. Note that the factorization of the numerator and the denominator of the transfer function was done by the method of time constants described in [30].
${{p}_{2,3}}=\zeta .\omega \pm j{{\omega }_{0}}\sqrt{1{{\zeta }^{2}}}$ (22)
${{\omega }_{0}}=\sqrt{\frac{{{a}_{1}}}{{{a}_{3}}}}$ (23)
$\zeta =\frac{{{a}_{2}}{{\omega }_{0}}}{2{{a}_{1}}}$ (24)
${{\omega }_{r}}={{\omega }_{0}}.\sqrt{12{{\zeta }^{2}}}$ (25)
As shown in Figure 8, the location of the poles and the RHP zero of the compensated frequency response for proposed LDO changes relatively with load current I_{L}. Figure 8 shows that the transfer function corresponding to the frequency response of the proposed compensated LDO also contains two other LHP poles p_{6} and p_{7} and two other LHP zeros z_{3} and z_{4}. In the case of the low load current, zero z_{3} cancels pole p_{6} and zero z_{4} cancels pole p_{7}. Furthermore, the stability analysis shows that for certain low values of I_{L}, the two complex conjugate poles move towards the right halfplane. Not shown in this paper, Cardan's method [31], allows to solve a cubic equation whose solutions give the poles p_{2,i }and p_{3,i }represented in Figure 8. To avoid this potential instability, the gate width Wp of the pass transistor Mp must meet the condition given by constraint (26), where C_{O}=C_{L}+C_{db,P }and C_{C,tot}=2C_{C}. C_{gs,ov }and C_{gd,ov }represent the overloop capacitance gatetosource and gatetodrain of M_{P}, respectively [29].
${{W}_{P}}\ge \frac{{{C}_{O}}+{{C}_{C,tot}}}{20{{C}_{gs,ov}}{{C}_{gd,ov}}}$ (26)
For the process used in the proposed design, C_{gd,ov}=C_{gs,ov}=330 pF/m. Generally C_{L}=100 pF and therefore we can neglect C_{db,P }in front of C_{L}, hence C_{O}≈C_{L}. If we choose C_{C}=1 pF, we find W_{P}≥16586,9 μm. In conventional LDO design, the minimum value of W_{P} is given by Eq. (27) [10], where I_{L,max} is the maximum output current supplied by an LDO regulator to the load, V_{DO} is the maximum dropout voltage and K_{p}’ represents a process transconductance parameter of PMOS transistor which is equal in technology used to 96.6 μA/V^{2}. For our design specifications, V_{DO,max}=150 mV and I_{L,max}=150 mA. If the M_{P} gate length L_{P} is set to its minimum value of 0.18μm, W_{P,min}=12422,36 μm. We observe that the minimum value of W_{P} given by Eq. (26) in proposed design, is greater than that given by Eq. (27) in conventional design. Thus, there is a compromise between the layout area occupied by M_{P} and the stability of the proposed LDO regulator system.
Figure 8. Polezero location in complex s plane for the proposed compensated LDO regulator
$\left(\frac{W_{P}}{L_{P}}\right)_{\min }=\frac{I_{L, \max }}{K_{p}^{\prime} V_{D O}^{2}}$ (27)
To show the robustness of the proposed compensation circuit, we evaluated the phase margin PM for all required values of the load current. The phase margin of the proposed LDO system is given by:
$\begin{align} & PM\approx 90{}^\circ {{\tan }^{1}}(\frac{{{\omega }_{UGF}}}{{{\omega }_{{{z}_{RHP}}}}})+{{\tan }^{1}}(\frac{{{\omega }_{UGF}}}{{{\omega }_{{{z}_{1}}}}})+{{\tan }^{1}}(\frac{{{\omega }_{UGF}}}{{{\omega }_{{{z}_{2}}}}}) \\ & \mathop{{}}^{{}}\mathop{{}}^{{}}\mathop{{}}^{{}}\mathop{{}}^{{}}{{\tan }^{1}}(\frac{{{\omega }_{UGF}}}{{{\omega }_{pd}}}){{\tan }^{1}}Q(\frac{{{\omega }_{UGF}}}{{{\omega }_{0}}}\frac{{{\omega }_{0}}}{{{\omega }_{UGF}}}) \\ & \mathop{{}}^{{}}\mathop{{}}^{{}}\mathop{{}}^{{}}\mathop{{}}^{{}}{{\tan }^{1}}(\frac{{{\omega }_{UGF}}}{{{\omega }_{p4}}}){{\tan }^{1}}(\frac{{{\omega }_{UGF}}}{{{\omega }_{p5}}}) \\ \end{align}$ (28)
To have a sufficient phase margin, it is necessary to place the zero z_{1} in the vicinity of the unity gain angular frequency ω_{UGF} and before the resonance angular frequency ω_{0} of the two conjugate complex poles, the second zero z_{2} is placed in the vicinity of ω_{0}. If, for example, we choose f_{UGF}=1 MHz and f_{z1}= 1.5f_{UGF}, from Eq. (15), we will have f_{z2}= 6.f_{UGF} and therefore f_{0}≈f_{z2}≈6 MHz. In this case, and according to Eq. (28), in the worst case where the positive real zero is displaced in the vicinity of the unity gain frequency, the phase margin obtained is equal to 80°. Therefore, the proposed compensation circuit ensures the stability of the LDO regulator for all required values of the load current which represents the desired result.
Finally, the stability condition on the phase margin PM for the proposed LDO regulator system, given by Eq. (29), allows determining the values of R_{C} and C_{C} for the desired value of unity gain frequency f_{UGF}.
$\begin{align} & PM\approx 90{}^\circ +{{\tan }^{1}}(2\pi {{f}_{UGF}}{{R}_{C}}{{C}_{C}}) \\ & \mathop{{}}_{{}}^{{}}\mathop{{}}_{{}}^{{}}\mathop{{}}_{{}}^{{}}+{{\tan }^{1}}(\frac{\pi {{f}_{UGF}}{{R}_{C}}{{C}_{C}}}{2}) \\ \end{align}$ (29)
3.3 Transient response analysis
Transient response is the dynamic performance of linear regulator [10]. It can be separated into two parts, one is form load variation, named as load transient response, and the other is from line variation, named as line transient response. A typical LDO regulator transient response to load changes is shown in Figure 9.
For an increase of load current by ΔI_{L}, the LDO output observes an undershoot ΔV_{O}, for a response time duration of Δt_{1}. The loop reacts to this load change and the output voltage settles in a time duration defined by reaction time also known settling time Δt_{2}. Minimizing Δt_{1}+Δt_{2} is a critical need for digital load applications. The LDO response time Δt_{1} depends on undershoot ΔV_{O}, output capacitance C_{O }and load current change ΔI_{L}, and can be expressed as:
$\Delta {{t}_{1}}={{C}_{O}}.\frac{\Delta {{V}_{O}}}{\Delta {{I}_{L}}}$ (30)
The settling time, Δt_{2} is determined by the openloop bandwidth ω_{pd} of the regulation loop and the slewrate (SR) at the gate of pass transistor MP and can be written as:
$\Delta {{t}_{2}}=\frac{2\pi }{{{\omega }_{pd}}}+SR$ (31)
with,
$SR={{C}_{G,P}}.\frac{\Delta {{V}_{G,P}}}{{{I}_{SR}}}$ (32)
where, ΔV_{G,P} and I_{SR} represent the voltage change and slewing current at the gate of M_{P}, and we have ΔV_{G,P} is proportional to ΔV_{O}.
The proposed compensation circuit also improves the transient response by increasing the bias current at the gate of the pass transistor M_{P} via the current amplifier block which amplifies this bias current I_{B,C} during the transient times of the load current, which allows to minimize the slewrate and consequently to reduce overshoots and undershoots and also to reduce the settling time.
Figure 9. Typical LDO Regulator Load Transient Response
3.4 Voltage reference
The LDO regulator proposed in this work also includes the voltage reference, which plays an important role in the accuracy of the feedback voltage V_{FB}, which is why this voltage reference V_{REF} must have a precise value and independent of the temperature, the supply voltage and the process of the technology used. The voltage reference designed for the LDO regulator was previously realized and published by the same authors [32]. The value of V_{REF} is equal to 0.635 V.
The proposed three stage LDO regulator with dual frequency compensation scheme was simulated in standard 0.18 µm CMOS process using Cadence Virtuoso Spectre Simulator.
As shown in Figure 10 in the DC line simulation at maximum load current of 150 mA, the proposed LDO provides a DC output voltage V_{O} of 1.2 V from a minimum input supply voltage V_{I} of 1.35 V. The DC line regulation is 4.68mV/V for input supply voltage variation ΔV_{I} of 0.5 V from 1.35 V to 1.85 V, this operating voltage range is limited by the line regulation of the designed voltage reference [32] as shown in Figure 10 (b).
(a) With ideal voltage reference
(b) With internal voltage reference
Figure 10. Simulation result of the DC line regulation at maximum load current
(a) Current efficiency
(b) Power efficiency
Figure 11. Simulation result of efficiency at maximum load current
As shown in Figure 11 in the DC efficiency simulation, for V_{I}=1.6, the current efficiency is equal to 99.9662 % while the power efficiency is 75 % at maximum load current of 150 mA, respectively.
Figure 12 gives the simulation result of the quiescent current. The quiescent current consumed by the proposed LDO regulator in full load condition and under the supply input voltage of 1.6 V is 10.75 µA without voltage reference, while this current is 50.75 µA with the internal voltage reference.
(a) With ideal voltage reference
(b) With Internal voltage reference
Figure 12. Simulation result of quiescent current
(a) DC load regulation
(b) Dropout voltage
Figure 13. DC load simulation result
As shown in Figure 13 in the DC load simulation, the DC load regulation is equal to 24.2 µV/mA at V_{I}=1.6 V measured from Figure 13 (a). The proposed LDO regulator has a low value of the dropout voltage less than 150mV for all required load current range as shown in Figure 13 (b).
(a) Transient line regulation for I_{L,max}=150 mA
(b) Transient load regulation for V_{I}=1.6 V
Figure 14. Transient simulation
Figure 14 presents the transient simulation of the proposed compensated LDO regulator. As shown in Figure 14 (a), for transient line regulation performed at maximum load current I_{L,max }of 150mA, the output voltage V_{O} presents an overshoot of 19.77 mV when the input supply voltage V_{I} pulse up from 1.35 V to 1.85 V during 1 µs of rise time, while V_{O} presents an undershoot of −17.15 mV when V_{I} pulse down from 1.85 V to 1.35 V during 1 µs of fall time. As shown in Figure 14 (b), for transient load regulation performed at input supply voltage V_{I} of 1.6 V, V_{O} presents an overshoot of 44.9 mV and an undershoot of −50.8 mV when load current pulse up from 0mA up to 150mA during 1 µs of rise time, while V_{O} presents an overshoot of 34.1 mV when load current pulse down from 150mA down to 0mA during 1 µs of fall time.
Figure 15 shows the open loop AC simulation for all required load current range at input supply voltage of 1.6V under C_{L}=100pF, R_{C}=100kΩ and C_{C}=1pF. The proposed LDO is stable for all required current load range. The minimum value of load current I_{L} for normal operation is 50 µA. The unity gain frequency is practically constant for any value of I_{L} in the required range and it is close to 1 MHz, which presents a good performance of the proposed compensation circuit. The AC magnitude exhibits a high frequency peak, its location depends on the value of the load current and this due to the presence of two complex conjugate poles as it has been proved in section 3. Table 1 summarizes the AC simulation performance for the proposed LDO regulator at input supply voltage V_{I} of 1.6 V.
Figure 15. AC open loop simulation for all required load current range
To show the robustness of the proposed dual compensation technique in term of stability with respect to the load current, a comparison with classical compensation methods and others compensation methods cited in this work such as [18] and [21] is performed as shown in Figure 16. The proposed compensation technique ensures stability not only for low values of the load current but also for very low values of the load current, in particular for a zero load current where the phase margin is equal to 45.1° as it is shown in Figure 16 (b). This result is not achieved by the compensation methods proposed in [18, 21]. In addition, the proposed compensation circuit uses a total compensation capacitance C_{C,tot }of 2 pF, while the authors of [18, 21] have used 23 pF and 41 pF respectively to guarantee good stability. The smaller the capacitor to integrate on the chip, the more the layout area is saved.
Table 1. AC simulation performance of the proposed LDO regulator at V_{I} =1.6V
Performance 
Mimum load 
Full load 
DC gain H_{0,c} 
72.53 dB 
74.05 dB 
Bandwidth f_{pd}^{ 1} 
268.3 Hz 
220.3 Hz 
Gainbandwidth product H_{0,c}. f_{pd} 
1.135 MHz 
1.110 MHz 
Unity gain frequency f_{UGF} 
1.139 MHz 
1.113 MHz 
Phase margin PM ^{2} 
84.06° 
92.08° 
Resonant frequency f_{r}^{3} 
6.309 MHz 
39.81 MHz 
^{1. }f_{pd}=2πω_{pd}. ^{2} PM=180°+Arg[H_{ol,c}(j2πf_{UGF})]. ^{3} f_{r} = f_{pd}=2πω_{r}
Table 2 summarizes performance characteristics of the proposed LDO regulator and comparison with others LDO regulators cited in this work is given. For comparison of the State of the Art, some Figures of Merit (FOMs) is proposed [33]. Note that the smaller the FOM chosen for this work, the better the regulator. The FOM chosen for the comparison is given by Eq. (33), where ΔV_{O,max} is the maximum variation of the output voltage V_{O} in the line voltage or the load current (maximum overshoot or absolute value of minimum undershoot), I_{Q} is the quiescent current, C_{L} is the load capacitance and I_{L,max }is the maximum load current.
$FOM=\left \Delta {{V}_{O,\max }} \right.\frac{{{C}_{L}}.{{I}_{Q}}}{I_{L,\max }^{2}}$ (33)
(a) all load current range
(b) low load current range
Figure 16. Phase margin versus load current for LDO regulator system
Table 2. Performance of proposed LDO regulator and comparison with other LDO regulators cited in this work
Performance 
[17] 
[25] 
[26] 
[27] 
[18] 
[22] 
This work 
Process (µm) 
0.35 
0.18 
0.35 
0.5 
0.065 
0.18 
0.18 
Input supply voltage V_{I} (V) 
3.04.0 
1.11.5 
1.21.5 
1.44.2 
1.2 
1.11.5 
1.351.85 
Output voltage V_{O} (V) 
2.8 
1.0 
1.0 
1.21 
1.0 
1.0 
1.2 
DropOut voltage V_{DO} @ I_{L,max }(mV) 
200 
100 
200 
200 
200 
114 
146.6 
Maximum load current I_{L,max }(mA) 
50 
50 
50 
100 
100 
100 
150 
Quiescent current I_{Q} @ I_{L,max }(µA) 
65 
54 
45 
45 
82.4 
20 
^{5}9.6811.3 ^{6}49.6851.3 
Current efficiency η_{I} @ I_{L,max} (%) 
99.935 
99.946 
99.955 
99.955 
99.917 
^{1}N. A. 
99.96899.967 
Power efficiency η @ I_{L,max} (%) 
^{1}N. A. 
^{1}N. A. 
^{1}N. A. 
^{1}N. A. 
^{1}N. A. 
^{1}N. A. 
88.865.5 
Minimum onchip output capacitance C_{L }(pF) 
10^{2} 
10^{2} 
10^{3} (Offchip) 
10^{5} (Offchip) 
10^{2} 
10^{2} 
10^{2} 
Total compensation capacitance C_{C,tot} (pF) 
23 
5 
41 


12 
2 
Transient Line Regulation (ΔV_{O} varying V_{I}) 


Maximum overshoot (mV) 
90 
^{1}N. A. 
^{1}N. A. 
23 
8.91 
55.66 
23.05 
Minimum undershoot (mV) 
−10 
^{1}N. A. 
^{1}N. A. 
−12 
−10.63 
−55.34 
−22.49 
Transient Load Regulation (ΔV_{O} varying I_{L}) 


Maximum overshoot (mV) 
80 
100 
70 
47 
0 
99.52 
31.1 
Minimum undershoot (mV) 
−80 
−80 
70 
−48 
−68.8 
591.1 
−54.5 
^{2 }Response time (µs) 
15 
2 
4 
5 
6 
6.3 
^{3}1,697 ^{4}1,994 
Internal Votlage Reference 
No 
No 
No 
No 
No 
No 
Yes 
DC Line Regulation @ I_{L,max} (mV/V) 
^{1}N. A. 
^{1}N. A. 
0.327 
^{1}N. A. 
4.7 
^{1}N. A. 
4.68 
DC Load Regulation (µV/mA) 
^{1}N. A. 
^{1}N. A. 
250 
408 
300 
1 
24.724.9 
FOM (fs) 
416 
388.8 
2520 
42750 
56.69 
118.2 
2.345^{7}12.03 
^{1}Not available, ^{2}Value obtained in load transient regulation, ^{3}Simulated value obtained at V_{I}=1.6 V for I_{L} stepup variation from 150 mA to 0 mA with 1 µs of rise time, ^{4}Simulated value obtained at V_{I}=1.6 V for I_{L} stepdown variation from 0 mA to 150 mA with 1 µs of fall time, ^{5 }Values obtained with ideal voltage reference, ^{6} Values obtained with internal voltage reference, ^{7 }Value obtained with internal voltage reference and calculated by using Eq. (32)
It is difficult to compare LDO regulators because generally each one is intended for a specific application. There are always tradeoffs between different performances such as high stability, fast transient response, low quiescent current which increases battery life and high power supply ripple rejection ratio which is not addressed in the proposed work. To determine the good LDO regulator from the performances inserted in Table 2, we base on the calculated value of the figure of merit FOM which includes the consumption from quiescent current, the capability of the LDO regulator to provide maximum current, the capacitance used to the output which must be as small as possible to save the surface and finally the maximum peak of the output voltage which must be minimized to avoid an abnormal operation of the circuit supplied by the LDO regulator. The proposed LDO regulator is better compared with the LDO regulators cited in the Table 2, because it has the smallest value of FOM which is equal to 2.345 fs with ideal voltage reference, while FOM is equal to 12.03 fs with internal voltage reference.
In this paper, a novel internally frequency compensation technique called dual frequency compensation is proposed to enhance stability and transient response of the onchip output capacitor three stage lowdropout linear voltage regulator. The proposed compensation technique guarantees the stability of the regulator system in a wide range of load current from 0 to 150 mA with small value of compensation capacitance of 2 pF and maximum value of 100 pF of load capacitance. The maximum quiescent current at full load condition of 150 mA is only 51.29 µA when LDO regulator operates with 1.8 V of input supply voltage. Based on the calculated value of the FOM, the proposed LDO regulator exhibits good performance in terms of transient response compared to LDO regulators cited in this paper. The proposed circuit can be used to power a low voltage system on a chip of a smart wearable device. The proposed compensation method in this work degrades the power supply ripple rejection of the LDO regulator due to the decrease in the value of the R_{G,P} resistance. This problem has not been studied in this paper and will be addressed in future work.
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