Figure 8.11(a) shows our complete regulated charge pump, which includes all of the circuitry that was discussed earlier in this Chapter. Instead of using linear resistors in the voltage divider, we use eight diode-connected pFETs, each in their own well. Figure 8.11(c) shows measurements of the current draw of the divider branch at different voltages. The divider branch is designed to draw 100nA–1àA over the typical operating range (10V–12.5V).
This current is enough to maintain stable regulation without unnecessarily wasting power.
The well-to-substrate breakdown current can be seen in the top-right of Fig. 8.11(c). This breakdown occurs at a much higher voltage than the operating voltage of the circuit, so it is not a concern.
By dividing Vout by a factor of eight in Fig. 8.11(a), Vout is thus regulated to 8Vtarg. The measured transfer curve from Vtarg to Vout is shown in Fig. 8.11(b). It can be seen that the output voltage is well-regulated from approximately 8V to 15V. Deviation at the high voltages is caused by the charge pump’s limited maximum voltage (N + 1)Vdd = 17.5V. In Fig. 8.11(a), error amplification is achieved by using an OTA to convert the the error into a current. Deviation at the low voltages in Fig. 8.11(b) is caused by the error-amplification OTA’s bias transistor being pushed out of the saturation region.
Now that the complete details of the regulated charge pump have been elaborated, we can calculate the loop gain K that was described in Section 8.2.2. Starting fromVout: Vout is divided by r = 8, then converted to a current with transconductance Gm, a current mirror scales this current by a factor of 4, the current-controlled oscillator then converts this current to a frequency with a gain of KRO = 2kHz/nA, and finally, the charge pump converts this frequency to the output voltage with a gain of KCP. The total loop gain is the product of all of these components
K = 4GmKROKCP
r (8.6)
The transconductanceGm provides a way to tune the charge pump for the desired loop gain, which changes the load-regulation characteristics and the start-up time. Using K and (8.2), we can obtain the closed-loop output resistance from Table 8.1
RCL = ROL
K = r
4CpGmKRO
N
(N + 1)Vdd−Vout (8.7)
Brandon D. Rumberg Chapter 8. Charge Pump 101
Charge Pump
Current-Controlled Ring Oscillator
Vtarg
1"=7R2
2"
clk 4-Phase Clk Gen
2.5V
Iload
(a)
Vfb Vout
4x IF
Edgifier
(b)
0.8 1 1.2 1.4 1.6 1.8 2 2.2
6 8 10 12 14 16
Vtarg (V) V out (V)
8*Vtarg Measured
0 5 10 15 20 25 30 35
10-12 10-10 10-8 10-6 10-4
Vout (V) IF (A)
(c)
Figure 8.11: (a) Block diagram of our complete regulated charge pump. (b) Measured dc- dependence of the charge-pump output on Vtarg. (c) Measured current–voltage sweep of the pFET-divider circuit.
To verify this expression, we have measured the open-loop and closed-loop load regulation in Fig. 8.12(a&b). The improvement afforded by regulation is clearly evident. Indeed, it would be very difficult to precisely generate an arbitrary high voltage without regulation.
The output impedance is extracted from this data and is shown in Fig. 8.12(c&d). Good agreement is found between the measured results and the theoretical values forROLandRCL. This agreement confirms that, when the charge pump is designed to sufficiently approach ideal characteristics, this simple analysis can be used to confidently design a high-voltage charge pump.
In a circuit, such as our charge pump, that operates beyond the rated voltage of the pro- cess, the designer should ensure that the local voltage differentials for each device are within the rated voltage range. One reason that compelled us to choose the charge pump circuit in Fig. 8.6(a) is that the use of two series switches in each stage protects the devices from any
105 106 103
104 105 106 107 108
Clock Frequency (Hz)
Output Resistance (Ω)
Measured Theory
20 40 60 80
103 104 105 106 107 108
Transconductance (àA/V)
Output Resistance (Ω)
Measured - Fresh Measured - 1M cycles Theory
(c) (d)
10-7 10-6 10-5 10-4
6 8 10 12 14 16
Load Current (A) V out (V)
10-7 10-6 10-5 10-4
6 8 10 12 14 16
Load Current (A) V out (V)
(a) (b)
clock = 1 MHz
clock = 20 MHz
Vtarg = 7V
Vtarg = 16V
Open Loop Closed Loop
Figure 8.12: Measured load regulation characteristics of our charge pump. (a) Open-loop with clock frequency ∈ [1MHz, 2MHz, 5MHz, 10MHz, 20MHz]. (b) Closed-loop with Vtarg varied from 7V to 16V in increments of 1V. Measured DC output impedance of our charge pump. (c) Open-loop as a function of clock frequency. (d) Closed-loop as a function ofGm. To validate reliability, the measurement was performed with a fresh charge pump, as well with a charge pump that had previously generated 106 12.5V-pulses.
voltage stress greater than Vdd [176]. To verify that this protection ensures reliable perfor- mance under typical operating conditions, we measured the charge pump’s output resistance before and after the charge pump had generated 106 12.5V-pulses of 1ms duration. These pulses are typical of the way the charge pump is used to program floating-gate transistors.
The before-and-after measured output resistance is shown in Fig. 8.12(d). The “burned in”
charge pump consistently has a slightly higher output resistance. However, the variation is
Brandon D. Rumberg Chapter 8. Charge Pump 103
0 200 400 600 800 1000 1200
0 5 10 V out (V)
0 200 400 600 800 1000 1200
0 5 10
Power (mW)
0 200 400 600 800 1000 1200
105 106 107
Frequency (Hz)
Time (às)
Figure 8.13: Measured transient characteristics of our closed-loop charge pump. (Top) Output voltage. (Middle) Supply current. (Bottom) Closed-loop adapted clock frequency.
small, and the number of cycles is greater than the typical rating for Flash memory, which confirms that this charge pump has great long-term reliability for our application.
The prominent characteristic of a frequency-regulated charge pump is that the frequency varies, which helps to minimize the power consumption once the target output voltage is reached. Figure 8.13 shows a measurement of the charge pump generating a 1ms, 12.5V tunneling pulse. The measured frequency over time is shown in Fig. 8.13(c). During startup, the OTA is saturated and the clock pumps at a maximum frequency of approximately 30MHz.
Once the target voltage is reached, the clock is relaxed to approximately 300kHz. The resulting mitigation in supply current while the voltage is held is seen in Fig. 8.13(b). The overall energy that was used to generate this pulse was 1.45àJ.
The efficiency of a charge pump is the power delivered at the output of the charge pump divided by the total power going into the circuit. For our regulated charge pump, this input power includes the power consumed by all components, not just the charge pump. We have not emphasized efficiency because it is not a crucial specification when generating short tunneling pulses for tunneling junctions that draw a very small load current. As can be seen in Fig. 8.13, most of the energy is consumed while starting up the charge pump. However, we will briefly discuss efficiency because it is a standard comparison point for voltage converters and because it will be of interest for modifying this charge pump to generate injection-level supply voltages.
From [168], the supply current of an ideal charge pump with bottom-plate stray capaci- tance is
Ivdd=
(N + 1) +α N2
(N+ 1)Vdd−VoutVdd
IL (8.8)
whereαis the ratio of the bottom-plate stray capacitance to the pumping capacitance, which is fixed for a given CMOS process and is in the range of 0.1–0.15 for our process [162]. The first additive term accounts for the current that is pumped toward the load. The second term accounts for the current that charges and discharges the stray capacitance. The theoretical maximum efficiency is
γ = ILVout
IvddVdd = Vout h
(N + 1) +α(N+1)VN2
dd−VoutVddi Vdd
(8.9) ForVout = 12V,N = 6, andVdd = 2.5V, the maximum theoretical efficiency is approximately 52%. Figure 8.14 shows the measured efficiency of the open-loop and closed-loop charge pump. The regulated charge pump was measured withVout = 12V. The charge pump achieves approximately 64% of the theoretical efficiency. Furthermore, the overhead of regulation has not significantly decreased the efficiency of the unregulated charge pump. In fact, variable- frequency regulation is able to achieve better regulation across a wider range of load currents.
10-6 10-5 10-4
20 22 24 26 28 30 32 34 36 38
Load Current (A)
Efficiency (%)
Closed loop Open loop
20 MHz 10 MHz 5 MHz
2 MHz 1 MHz
Figure 8.14: Measured efficiency of the charge pump.
Since the charge pump is designed for use in wireless sensor networks, where the supply voltage is supplied by batteries or energy harvesting and may be unstable, power-supply rejection is an important concern. Figure 8.15 shows the measured power supply rejection of the open-loop and closed-loop charge pumps. The use of regulation improves the power- supply rejection by 68dB. The regulated charge pump was measured with Vout = 12V.
Table 8.4 compares our charge pump with other high-voltage charge pumps. Aaltonen’s charge pump [174] is the only regulated high-voltage charge pump that we are aware of that presents quantitative performance specifications. As a point of comparison, we have also included Li’s charge pump [176], which is unregulated, but which is the circuit upon which we have based our charge pump stages [Fig. 8.6(a)]. Applying our regulation loop to that charge pump would improve many of its performance parameters by a factor of the loop gain.
Brandon D. Rumberg Chapter 8. Charge Pump 105
101 102 103 104 105
−20
−10 0 10 20 30 40 50 60
Frequency (Hz)
Power Supply Rejection (dB)
Regulated Unregulated
Figure 8.15: Measured power-supply rejection of our charge pump. Closed-loop regulation improves power-supply rejection by 68dB.
Table 8.4: Comparison of High-Voltage Charge Pumps
Tech Vdd Vout N TotalC Size RO γ IL FOM
Ours 0.35àm 2.5V 12.5V 6 18pF 0.069mm2 6.8kΩ 33% 25àA 4.08ì107 Aaltonen [174] 0.35àHV 2.5V 10V 9 14.4pF 0.14mm2 23kΩ 18% 29àA 1.21ì107 Li [176] 0.18àm 1.8V 7V 4 80pF sims only 93kΩ 70% 13àA 0.05ì107
In the Table, IL is the load current at which the parameters are specified. RO is the closed-loop output resistance for the first two entries, and is the open-loop output resistance for the last entry, since it was unregulated. For easy comparison, we suggest the following figure-of-merit
FOM = Vout
VddCCPRO (8.10)
where CCP is the total pumping capacitance. A higher FOM value is better. This figure- of-merit definition rewards large voltage step-up ratios, low output resistance, and small size—all of which are important for generating tunneling voltages. However, we should note that the comparison charge pumps were not designed for generating tunneling voltages:
Aaltonenen’s charge pump was designed for an electrostatic actuator for MEMS and Li’s charge pump had no specific design purpose.