The present application is generally related to lighting systems. In particular, the present application is directed to systems and methods for providing a hysteresis based driver that incorporates the forward voltage of a light emitting device (LED).
Lighting systems may include light emitting devices organized in various configurations depending on the illumination applications. The LEDs are semiconductor devices that have a forward voltage. Different LEDs may have different forward voltages which may further vary based on operation of the LED. As LEDs heat up, the forward voltage drops and the current passing through the LED increases. For a given temperature, a small change in forward voltage can product a disproportionally large change in forward current. Also, the forward voltage required to achieve a desired light output can vary with LED die size, die materials, lot variations and temperature. In a circuit with LEDs and without regulation, the current will increase with an increase in supply voltage and/or a decrease in LED forward voltage, and, conversely, will decrease with a decrease in supply voltage and/or an increase in LED forward voltage.
The present disclosure is directed to a hysteresis based driver that incorporates the forward voltage of the LEDs being driven into the design of the driver itself. Instead of providing a typical fixed voltage reference, the forward voltage of one or more LEDS driven by the driver is used as a voltage reference. Using the LED voltage as a voltage reference may provide a stable voltage reference. Although the forward voltage of the LEDs is varying, relative to the widely varying supply voltage, the forward voltage of the LEDs can be considered stable. As the input voltage varies during operation of the one or more LEDs, the current varies as well. This current change is larger than it would be without the LEDs and only resistors. This variable current measurement may be used as input into a hysteresis circuit that controls the switch that turns on and off the one or more LEDs. As such, the driver may not incorporate or use a typical fixed voltage reference such as one provided by a zener diode.
The design and construction of this hysteresis based driver provides a variety of advantages. As the variability of the forward voltage Vfa-n of the light sources changes less dramatically or smaller than the corresponding changes in the input voltage, this provides a variable but stable input into the hysteresis based determinations that drive the frequency of switching off and on the switch. With the continuous variability of the reference signal, the driver provides an automatic frequency spectrum in which the frequency of operation automatically changes and without setting a frequency. This also provides a signal to the light sources that comprises a variable frequency during on time with a constant off time. As a result, there is randomization to the current drawn by the light sources.
In some aspects, the present solution is directed to a driver for one or more light emitting diodes (LEDs) that incorporates forward voltage of the one or more LEDs to provide hysteresis. The driver may include a first input to receive an input voltage and a switch electrically coupled to the first input and electrically coupled to one or more light emitting diodes (LEDs). An output of the switch, when switched on, to provide voltage to the one or more LEDs. The driver may include a current measurement component electrically coupled to the one or more LEDS to measure current through the one or more LEDs based on forward voltage of the one or more LEDs. The driver may include a hysteresis component to receive as input the input voltage and a measurement of voltage based on the current measured by the current measurement component. The current measurement component is configured to measure changes to the current based on changes to the forward voltage of the one or more LED. The hysteresis component is electrically coupled to the switch to turn the switch off and on responsive to changes to the input voltage in conjunction with the changes to the forward voltage of the one or more LEDs, as measured by the current measurement component, being above or below a threshold.
In some embodiments, the driver comprises a ballast resistor electrically coupled to an output of the switch. The ballast resistor comprising a predetermined resistance to provide a current, when the switch is on, to the one or more LEDs below the maximum rating of the one or more LEDs. In some embodiments, the hysteresis component comprises a comparator that compares the input voltage to the measurement of voltage based on the current measured by the current measurement component. In some embodiments, the hysteresis component further comprises a feed forward resistor electrically coupled between input and output of the comparator. The feed forward resistor comprises a predetermined resistance that provides a smaller effect than the input voltage to the comparator and a larger effect than an offset voltage of the comparator. In some embodiments, the driver comprises a filter electrically coupled between the current measurement component and the hysteresis component to provide a filtered version of the current measurement from the current measurement component as input to the hysteresis component. The filter is configured to have a predetermined oscillation frequency to avoid exceeding a threshold of the switch. In some embodiments, the current measurement component includes a current sense resistor to convert into voltage the measurement of current through the one or more LEDs. In some embodiments, the current to the one or more LEDs is regulated as the voltage output from the one or more LEDs changes with a lesser effect than changes to the input voltage.
In some aspects, the present solution is directed to a driver for one or more light emitting diodes (LEDs) that uses forward voltage of the one or more LEDs as a reference voltage. The driver includes a first input to receive an input voltage and a switch electrically coupled to the first input and electrically coupled to one or more light emitting diodes (LEDs). An output of the switch, when switched on, to provide voltage to the one or more LEDs. The driver also includes a measurement component electrically coupled to the one or more LEDs to measure current through one or more LEDs based on changes to the input voltage. The driver includes a comparator to receive as a reference voltage a measurement of voltage from the measurement component, the comparator configured to compare the reference voltage to the input voltage. The comparator is electrically coupled to the switch to turn the switch off and on responsive to comparison of the input voltage to the reference voltage comprising forward voltage of the one or more LEDs.
In some embodiments, the driver comprises a ballast resistor electrically coupled to an output of the switch. The ballast resistor has a predetermined resistance to provide a current, when the switch is on, to the one or more LEDs below the maximum rating of the one or more LEDs. In some embodiments, the driver included a feed forward resistor electrically coupled between input and output of the comparator. The feed forward resistor has a predetermined resistance that provides a smaller effect than the input voltage to the comparator and a larger effect than an offset voltage of the comparator. In some embodiments, the driver included a filter electrically coupled between the measurement component and the comparator to provide a filtered version of the current measurement from the measurement component as input to the comparator. The filter may be configured to have a predetermined oscillation frequency to avoid exceeding a threshold of the switch. In some embodiments, the measurement component includes a current sense resistor to convert into voltage the measurement of current through the one or more LEDs. The changes to the forward voltage of the one or more LEDs provides a stable reference voltage to the comparator. In some embodiments, the driver does not have a reference voltage for the comparator other than a stable reference voltage provided by changes to the current through the one or more LEDs.
In some aspects, the present solution is directed to a driver for one or more light emitting diodes (LEDs) that automatically provides varying frequency. The driver includes a first input to receive an input voltage and a switch electrically coupled to the first input and electrically coupled to one or more light emitting diodes (LEDs). An output of the switch, when switched on, to provide voltage to the one or more LEDs. The driver includes a measurement component electrically coupled to the one or more LEDs, to measure voltage across the one or more LEDs based on changes in forward voltage of the one or more LEDs. The driver includes a hysteresis component to receive as input the input voltage and a measurement of voltage responsive to the current measurement component. The measurement component is configured to measure voltage output from the one or more LEDs responsive to changes to the input voltage. The hysteresis component is electrically coupled to the switch to turn the switch off and on responsive to the changes to the voltage output, the voltage output to increase with a larger effect than changes to the input voltage. The driver is configured to have times the switch is on vary based on changes to the input voltage.
In some embodiments, the hysteresis component comprises a comparator and a feed forward resistor electrically coupled between input and output of the comparator, the feed forward resistor comprising a predetermined resistance that provides a smaller effect than the input voltage to the comparator and a larger effect than an offset voltage of the comparator. In some embodiments, the driver includes a filter electrically coupled between the measurement component and the hysteresis component to provide a filtered version of the current measurement from the measurement component as input to the hysteresis component. The filter may be configured to have a predetermined oscillation frequency to avoid exceeding a threshold of the switch. During a charging part of oscillation the filter reacts more quickly as the input voltage increases and the oscillation varies inversely with input voltage. In some embodiments, the measurement component includes a current sense resistor to convert into voltage the measurement of current through the one or more LEDs.
The foregoing and other objects, aspects, features, and advantages of the present invention will become more apparent and better understood by referring to the following description taken in conjunction with the accompanying drawings, in which:
The features and advantages of the present invention will become more apparent from the detailed description set forth below when taken in conjunction with the drawings, in which like reference characters identify corresponding elements throughout.
Referring now to
The design and construction of this hysteresis based driver provides a variety of advantages. Instead of dealing with the challenges of changes to forward voltages of light sources, such as LEDs, the driver incorporates and leverages the forward voltage into the design and operation of the driver. The driver uses the forward voltage from the light sources as a variable voltage reference signal 115 and thus does not need to use a fixed voltage reference signal such as a zener diode typical to most applications. As the variability of the forward voltage Vfa-n of the light sources changes less dramatically or is smaller than the corresponding changes in the input voltage, this provides a variable yet stable input into the hysteresis based determinations that drive the frequency of switching off and on the switch. With the continuous variability of the reference signal, the driver provides an automatic frequency spectrum 155 in which the frequency of operation automatically changes and without setting a frequency. This also provides a signal 108 to the light sources that comprises a variable frequency during on time with a constant off time. As a result, there is randomization to the current drawn by the light sources.
The driver may include, be electrically coupled to or drive one or more light sources 110A-N connected to each other. In some embodiments, light source is any type and form of semiconductor or device that produces or emits a light. In some embodiments, light source 110 is a semiconductor light emitting device emitting light of any spectral or wavelength range. In some embodiments, light source is a LED. In some embodiments, light source 110 is an OLED, PHOLED, QDLED, or any other variation of a light source 110 utilizing an organic material. In some embodiments, each light source has the same forward voltage (Vf) or Vf profile. In some embodiments, each light source has a different forward voltage (Vf) or different Vf profile. A Vf profile may identify the change and/or rate of change to the Vf of a light source responsive to changes in operating conditions, such as input voltage, current and/or temperature.
In other embodiments, a light source 110 is a fluorescent light. In a number of embodiments, light source 110 is a lamp or a light bulb. In many embodiments, light source is a white light emitting diode. In a plurality of embodiments, the light source 110 is a broadband lamp or a broadband light source. In number of embodiments, the light source 110 is a black light. In a plurality of embodiments, light source 110 is a hollow cathode lamp. In a number of embodiments, light source 110 is a fluorescent tube light source. In some embodiments, the light source 110 is a neon or argon lamp. In a plurality of embodiments, light source 110 is a plasma lamp. In certain embodiments, light source 110 is a xenon flash lamp. In a plurality of embodiments, light source 110 is a mercury lamp. In some embodiments, light source 110 is a metal halide lamp. In certain embodiments, light source 110 is a sulfur lamp. In a number of embodiments, light source 110 is a laser, or a laser diode. In certain embodiments, light source 110 is a monochromatic light source. In a number of embodiments, light source 110 is a polychromatic light source. In a plurality of embodiments, light source 110 is a light source emitting light partially in the spectral range of ultraviolet light. In some embodiments, light source 110 is a device, product or a material emitting light partially in the spectral range of visible light. In a number of embodiments, light source 110 is a device, product or a material partially emanating or emitting light in the spectral range of the infra red light. In a number of embodiments, light source 110 is a device, product or a material emanating or emitting light in the visible spectral range. In some embodiments, light source 110 includes a filter to control the spectral range of the light emitted from the light source 110. In certain embodiments, light source 110 includes a light guide, an optical fiber or a waveguide through which light is emitted from the light source 110. In some embodiments, light source 110 includes one or more mirrors for reflecting or redirecting of light. In some embodiments, lighting device 110 reflects light emitted from another light source. In some embodiments, light source 110 includes a light reactive material affecting the light emitted, such as a polarizer, filter or a prism. In a plurality of embodiments, light source 110 is a coherent light source. In some embodiments, light source 110 is an incoherent light source.
In further details, the power 105 may be from any type and form of power source. The power supply may supply electrical power to the electrical load of the driver. The driver may be designed and constructed to be coupled, connect or receive power from the power supply 105. In some embodiments, the driver includes or incorporates the power supply. In some embodiments, the power supply may be a stand alone device. The power 105 may be AC or DC based. The power supply may be battery based. In some embodiments, a bridge rectifier is used to convert an AC signal input into a DC output signal. The DC output signal from the rectifier may be used as the power 105 providing the Vin to the driver. The DC output signal may be provides as input to the power source, such as a power regulator. The power supply may be regulated in that the output voltage and/or current is controlled or managed to a specific value or range.
The switch 120 may comprise any type and form of electrical component that can interrupt the current or divert the current from one conductor to another conductor. The switch may be electrically coupled to receive Vin or current from the power source 105. The switch may be electrically coupled to the hysteresis component to receive output from the hysteresis component as an input to the switch 120 to switch off and on. The frequency of switching between on and off may be driven or controlled by the hysteresis component. The switch may be electrically coupled to provide, when the switch is closed (On), current or Vin to the one or more light sources. When the switch is open (Off), the switch interrupts or diverts the current or Vin to the one or more light sources.
The switch may include or be electrically coupled in parallel to bypass circuitry, such as a pull-up or pull-down resistor, generally referred to herein as a bypass resistor. When the switch is open (off), the bypass resistor provides an input state to the circuitry connected to the light sources when no signal source, such as Vin, is connected. The bypass resistor prevents the voltage input from floating when the switch is open and Vin is not connected.
The output of the switch and/or bypass circuitry is electrically coupled to the one or more light sources. The output of the switch and/or bypass circuitry may be electrically coupled with a ballast 122 between the switch and light sources. The ballast may comprise an electrical component, such as a resistor, to limit the amount of current in the electrical circuit, such as current delivered or provided to the light sources. The ballast may be designed, constructed or configured to limit the current through the light sources to within a predetermined range or limit of the light sources, or otherwise to a desired level. The resistance value of the ballast resistor may be selected such that at the highest value of Vin, the current to the light sources when the switch is on is below the maximum rating of the light sources.
In some embodiments, an inductor 125 and diode 126 may be electrically coupled between the switch and/or bypass circuitry and/or the ballast and/or light sources. The inductor may comprise an electrical component to emphasize or filter certain frequencies of the signal, such as the output from the switch or bypass resistor. In some embodiments, the inductor may be used to filter out higher frequencies. In some embodiments, the inductor may be used to emphasize lower frequencies. The inductor may be designed and constructed to delay and reshape the signal (e.g., current), when current and/or voltage changes with time from the output of the switch and/or bypass circuitry. In some embodiments, any electrical circuitry providing a storage element or capacity may be included in the driver at the output of the switch. This may for example provide a buffer or otherwise implement a desired delay or signal shaping.
The light sources 110A-110N (generally referred herein as light source 110) may be electrically coupled between the switch and/or ballast and the measurement component 120. The light sources may each have a forward voltage Vf based on the material, design and construction of the light source. The Vf for each light source may change during operation of the light source, such as by changes in temperature, for example, heating and cooling. The Vf for each light source may be the same or different. The Vf for each light source may be within a predetermined range and/or in accordance with a forward voltage profile of the light source. The aggregate voltage drop across the light sources may be Vfa-n or the sum of Vfs of each light source.
The measurement component 130 may comprise any type and form of electrical circuitry or components to measure the voltage drop or Vfa-n across the light sources, such as via a current or voltage measurement. The measurement component may be electrically coupled to the one or more light sources. In some embodiments, the measurement component may be designed and constructed to measure the voltage output from or across the one or more light sources. In some embodiments, the measurement component may be designed and constructed to be a current measurement component to measure current outputted or passing through the one or more lights sources. In some embodiments, the current measurement component may convert the current measurement into a voltage. In some embodiments, the measurement component may comprise a resistor to sense the current passing through the light sources and converting the current into a voltage. The measurement component, such as a current sense resistor, may be electrically coupled to ground.
A filter 140 may be electrically coupled between the measurement component 120 and the hysteresis component 150. The filter may comprise any type and form of electrical circuitry or components to filter the measurement from the component measurement and providing a filtered version of this measurement to the hysteresis component. In some embodiments, the filter may comprise an RC (resistor-capacitor) circuit. RC circuits can be used to filter a signal by blocking certain frequencies and passing others, such as acting a high pass filter and/or low pass filter or band-pass filter. In some embodiments, the filter may comprise an RLC (resistor-inductor-capacitor) circuit. The capacitor of the filter may be selected or designed so that the oscillation frequency is slow enough not to overwork or overheat the switch but fast enough not to cause visible flashing to the naked eye. The filter may be designed and constructed to provide what may be referred to as a hysteresis band for driving the hysteresis component and the operation of the switch to operate within a band of certain frequencies.
The hysteresis component 150 may comprise any type and form of electrical circuitry or electrical components for controlling the switching of the switch based on a comparison between voltages in the electrical circuitry of the driver, such as the voltage input Vin and the measurement of Vfa-n from the measurement component. The hysteresis component may comprise an electrical comparator that compares two current or voltages and outputs the higher of the two. The hysteresis component may compare one input current or voltage to be above or below a threshold comprising a reference current or voltage. For example, the hysteresis component may compare the input voltage to a threshold comprising the variable voltage reference signal provided via the forward voltage Vfa-n.
In some embodiments, the hysteresis component comprises an op-amp comparator. In some embodiments, the hysteresis component comprises a voltage comparator chip. The output of the comparison may be electrically coupled to the switch to turn the switch on and off. The output of the comparison may be electrically coupled to an op-amp inverter, electrical buffer or gate electrically coupled to the switch.
The comparator of the hysteresis component may compare the voltage input, Vin, or a version of Vin, to the variable voltage measurement, or a version of the variable voltage measurement, from the forward voltage Vfa-n measured by the measurement component. The comparator of the hysteresis component may compare a version of the voltage input to a mixed signal, such as a combination of the variable voltage measurement with an output of the comparator through a feedback loop or circuitry.
As the hysteresis component receives and uses the variable voltage across the light sources, this provides historical input, data and measurements to provide a hysteresis based circuitry, control and driver. The variable voltage reference signal 115 will change over the course of operating and driving the light sources from a combination of changes to the voltage input and the changes in Vf of each of the light source responsive to the voltage input and the forward voltage profile of the light source.
As the hysteresis component receives and uses output of the comparator as a portion of input back into the comparator, this also provides another form of a hysteresis based circuitry, control and driver. The variable voltage reference signal 115 will further change over the course of operating the driver as the hysteresis circuitry will randomize the frequency of switching the switch on and the current drawn by the light sources. With the randomized frequency of how long the switch may be on (closed), the signal driving the light sources comprises a variable frequency on time with a constant off time signal 108. The design of the driver is configured to have times the switch is on vary based on changes to the input voltage. With the switch on time being at a randomized frequency and the resulting signal 108 having a variable frequency on time, the driver operates under and provides an automatic frequency spectrum 155. The frequency spectrum may comprise a range of different frequencies, such as within a band provided by the filter 140 and hysteresis component 150. The range of different frequencies are driven by the using the variable voltage reference signal 115 in combination with the filter and hysteresis component.
The driver 100 and/or hysteresis component may not use or incorporate a fixed voltage reference, such as zener diode which provides a fixed voltage over a wide range of currents. Instead of using a fixed voltage reference signal the driver and/or hysteresis component incorporates and uses the variable voltage output as a form of a hysteresis based reference for the comparator and to drive the switch.
The hysteresis component may include a mixer component to mix the signal received from the filter based on the measurement component with the output provided by the comparator or otherwise the hysteresis component. The mixer component may include a resistor electrically coupled between the filter and to one or more of: an input of the hysteresis component such as one of the inputs to a comparator and the output of the comparator such as via a feed forward resistor.
The hysteresis component may include a feedback loop electrically coupled between the output of the comparator and one of the inputs to the comparator. The feedback circuitry may include a resistor referred to as a feed forward resistor. The feedback circuitry may use the output of the comparator as part of the signal to an input of the comparator. The feedback circuitry may mix the signal from the output of the comparator with a version of the forward voltage measurement provided by the measurement component via the filter.
In some embodiments, the hysteresis component may receive the Vin signal or power from the power supply via a power supply compensator 107. The power supply compensator may comprise any type and form of electrical circuitry to provide a non-zero voltage input to the hysteresis component. The power supply compensator may comprise one or more resistors. The power supply compensator may be electrically coupled to ground.
In some embodiments of the design, construction or configuration of the driver circuitry, selected types and values of certain components may be used to facilitate, support or cause the desired operation and behavior of the driver. In some embodiments, the ballast resistor is selected to have a predetermined resistance so that, at the highest value of Vin, the current in the LEDs when the Switch is on is below the maximum rating of the LED. For example, this can be 10 to 30 Ohms typically, depending on LED current and Vin magnitude. In some embodiments, the capacitor of the filter is selected or configured to have a predetermined oscillation frequency that is below an operating or performance threshold of the switch, such slow enough to not overwork or overheat switch but fast enough to not cause visible flashing to the naked eye. For example, the capacitor can be 0.01 uF to 0.1 uF. In some embodiments, the capacitor and the design of the driver may be constructed or configured so that during a charging part of oscillation the filter reacts more quickly as the input voltage increases. In some embodiments, the capacitor and the design of the driver may be constructed or configured so that oscillation varies inversely with input voltage.
In some embodiments, the resistor of the filter may have a predetermined resistance, such as between 10 k to 50 k ohms. In some embodiments, the mixer filter may have a predetermined resistance that is the same as the filter resistor or may otherwise be in 10 k to 50 k ohms range. The resistance network of the power supply compensator may be designed and configured to have a predetermined resistance that creates a non-zero voltage at E. This can be 50 k and 5 k Ohms to ground or 10 k and 5 k Ohms to ground, depending on Vin magnitude. In some embodiments, the feed forward resistor is selected or configured to a predetermined resistance that causes it to have an effect much smaller than E but much larger than the offset voltage of the comparator. This may be in the 1 M Ohm range.
Referring now to
The light sources 110A-110N comprises LED1-LEDX electrically coupled between the measurement component 130 and the output of the switch and/or bypass resistor via a ballast resistor. The light sources 110A-110N comprise a voltage drop in the driver circuitry of a forward voltage of Vfa-n. The measurement component 130 measures the current passing through the light sources and provides this measurement signal to the filter 140, which in turn mixes the signal with the output of the comparator of the hysteresis component via the feed forward resistor. This mixed signal is provided as one voltage input to the comparator while the other voltage input to be compared is received from the power supply compensator. The output of the comparator is provided to the switch, such as via an inverter or buffer gate. The output of the comparator drives the switch on or off, which in turns either provides an off signal via the bypass resistor on an on signal via Vin. The signal 108 from the switch drives the one or more light sources, which in turn provides the forward voltage Vfa-n, which in turns provides the variable voltage reference to the hysteresis component. This variable voltage reference may be considered stable or fixed relative to the wide changes in the voltage supply or input voltage.
Based on the design and construction of the driver, the current change through the LEDs for a given input voltage change is larger than it would be without the forward voltage of the LEDs. This acts like negative feedback when the current is fed to the hysteresis component or the comparator. The voltage reference, for example at power supply compensator 107, acts like positive feedback to the hysteresis component or the comparator. When the negative and positive cancel out, there is regulation of the current.
Referring now to both
Referring to
In further details of step 205, initially, for example at time zero, the switch is off, which may be an initial default state. The voltage at each of nodes, B, C, and D is zero. The resistor network Y may comprises the resistance of and the resistors related to or making up the power supply compensator 107. The resistor network Z may comprise the resistors related to the feed forward resistor and the mixer resistor and which resistance may be equal to the feed forward resistance divided by the mixer resistance. The resistance network Z may be selected or configured to be much larger than the resistance network Y. Node E=A/Y while node F=D+G/Z.
At step 210, the comparator of the hysteresis component compares node E (A/Y) voltage to node F voltage (D+G/Z). Responsive to and as a result of the comparison, the output of the comparator, node G voltage, goes low and turns on the switch. Upon turning on the switch, node B voltage is equal to voltage at node A and node C is equal to the current in or passing through the LEDs. The voltage measurement at node C may be computed as follows:
C=((B−(voltage LEDs))/(Ballast+Current Sense))*(Current Sense).
As a result of the switch going on and the resulting electrical flow of voltage/current, the measurement at node F changes to F=D−G/Z.
At step 215, the capacitor in the filter starts charging. Responsive to the capacitor charging, the voltage at node D starts rising. As a result of node D voltage rising, the voltage at node F also rises. When voltage F=D−G/Z becomes higher than the voltage at node E=A/Y compared by the hysteresis component, the output of the hysteresis component changes to a high state. Response to the output at node G going high, the switch is turned off. As a result, the voltage at node F becomes F=D+G/Z
At step 220, with the switch off, voltage at nodes B and C become zero. The capacitor of the Filter starts discharging and voltage at D starts falling. As a result, the voltage at node F starts falling as well. When voltage F becomes lower than E=A/Y, the output at Node G of the hysteresis component changes to low state and causes the switch to turn on. The resulting voltage at node F. The cycle repeats between steps 215 and step 220.
Current regulation occurs because the voltage at node C changes with a much larger effect than node A changes due to the presence of forward voltage Vfa-n of light sources in the equation for node C. Therefore, node D also changes with a much larger effect than node A. This causes the filter to react more quickly as the voltage at node A rises. However, this effect is only for the rising (charging) part of the oscillation. The falling (discharging) part of the oscillation always occurs at the same rate because it is only dependent on voltage E. The result is that the oscillation always has a near to constant off time, but on time varies inversely with voltage. This causes a large inverse effect which is partly compensated for by the change in voltage at node E and the change in voltage at node G.
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