Note the following details of the code protection feature on Microchip devices:
YSTEM
CERTIFIED BY DNV
== ISO/TS 16949==
•Microchip products meet the specification contained in their particular Microchip Data Sheet.
•Microchip believes that its family of products is one of the most secure families of its kind on the market today, when used in the
intended manner and under normal conditions.
•There are dishonest and possibly illegal methods used to breach the code protection feature. All of these methods, to our
knowledge, require using the Microchip products in a manner outside the operating specifications contained in Microchip’s Data
Sheets. Most likely, the person doing so is engaged in theft of intellectual property.
•Microchip is willing to work with the customer who is concerned about the integrity of their code.
•Neither Microchip nor any other semiconductor manufacturer can guarantee the security of their code. Code protection does not
mean that we are guaranteeing the product as “unbreakable.”
Code protection is constantly evolving. We at Microchip are committed to continuously improving the code protection features of our
products. Attempts to break Microchip’s code protection feature may be a violation of the Digital Millennium Copyright Act. If such acts
allow unauthorized access to your software or other copyrighted work, you may have a right to sue for relief under that Act.
Information contained in this publication regarding device
applications and the like is provided only for your convenience
and may be superseded by updates. It is your responsibility to
ensure that your application meets with your specifications.
MICROCHIP MAKES NO REPRESENTATIONS OR
WARRANTIES OF ANY KIND WHETHER EXPRESS OR
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OTHERWISE, RELATED TO THE INFORMATION,
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Microchip received ISO/TS-16949:2009 certification for its worldwide
headquarters, design and wafer fabrication facilities in Chandler and
Tempe, Arizona; Gresham, Oregon and design centers in California
and India. The Company’s quality system processes and procedures
are for its PIC
devices, Serial EEPROMs, microperipherals, nonvolatile memory and
analog products. In addition, Microchip’s quality system for the design
and manufacture of development systems is ISO 9001:2000 certified.
®
MCUs and dsPIC® DSCs, KEELOQ
®
code hopping
QUALITY MANAGEMENT S
Trademarks
The Microchip name and logo, the Microchip logo, AnyRate, AVR,
AVR logo, AVR Freaks, BitCloud, chipKIT, chipKIT logo,
CryptoMemory, CryptoRF, dsPIC, FlashFlex, flexPWR, Heldo,
JukeBlox, KeeLoq, Kleer, LANCheck, LINK MD, maXStylus,
maXTouch, MediaLB, megaAVR, MOST, MOST logo, MPLAB,
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trademarks of Microchip Technology Incorporated in the U.S.A.
and other countries.
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mTouch, Precision Edge, and Quiet-Wire are registered
trademarks of Microchip Technology Incorporated in the U.S.A.
Adjacent Key Suppression, AKS, Analog-for-the-Digital Age, Any
Capacitor, AnyIn, AnyOut, BodyCom, CodeGuard,
CryptoAuthentication, CryptoAutomotive, CryptoCompanion,
CryptoController, dsPICDEM, dsPICDEM.net, Dynamic Average
Matching, DAM, ECAN, EtherGREEN, In-Circuit Serial
Programming, ICSP, INICnet, Inter-Chip Connectivity,
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motorBench, MPASM, MPF, MPLAB Certified logo, MPLIB,
MPLINK, MultiTRAK, NetDetach, Omniscient Code Generation,
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DS50002853A-page 4 2019 Microchip Technology Inc.
dsPIC33CH512MP506 DIGITAL
POWER PIM USER’S GUIDE
Preface
NOTICE TO CUSTOMERS
All documentation becomes dated, and this manual is no exception. Microchip tools and
documentation are constantly evolving to meet customer needs, so some actual dialogs
and/or tool descriptions may differ from those in this document. Please refer to our website
(www.microchip.com) to obtain the latest documentation available.
Documents are identified with a “DS” number. This number is located on the bottom of each
page, in front of the page number. The numbering convention for the DS number is
“DSXXXXXXXXA”, where “XXXXXXXX” is the document number and “A” is the revision level
of the document.
For the most up-to-date information on development tools, see the MPLAB
Select the Help menu, and then Topics to open a list of available online help files.
®
IDE online help.
INTRODUCTION
This chapter contains general information that will be useful to know before using the
dsPIC33CH512MP506 Digital Power Plug-In Module (PIM). Items discussed in this
chapter include:
• Document Layout
• Conventions Used in this Guide
• Recommended Reading
• The Microchip Website
• Product Change Notification Service
• Customer Support
• Document Revision History
DOCUMENT LAYOUT
This document provides an overview of the dsPIC33CH512MP506 Digital Power PIM.
The document is organized as follows:
• Chapter 1. “Overview” — This chapter introduces the dsPIC33CH512MP506
Digital Power PIM and provides a brief overview of its various features.
•
Appendix A. “Board Layout and Schematics”
schematics and the board layouts for the dsPIC33CH512MP506 Digital Power PIM.
• Appendix B. “Bill of Materials (BOM)” — This appendix presents the Bill of
Materials for the dsPIC33CH512MP506 Digital Power PIM.
• Appendix C. “Characterization Data” — This appendix provides
characterization data and guidance on sub-circuits of
Digital Power PIM
Choice of mutually exclusive
arguments; an OR selection
Represents code supplied by
user
“Save project before build”
4‘b0010, 2‘hF1
any valid filename
[options]
errorlevel {0|1}
var_name...]
void main (void)
{ ...
}
DS50002853A-page 6 2019 Microchip Technology Inc.
RECOMMENDED READING
This user’s guide describes how to use the dsPIC33CH512MP506 Digital Power PIM.
Other useful document(s) are listed below. The following Microchip document is
available and recommended as a supplemental reference resource:
• “dsPIC33CH128MP508 Family Data Sheet” (DS70005319)
Refer to this document for detailed information on the dsPIC33CH Dual Core
Digital Signal Controllers (DSCs). Reference information found in this data sheet
includes:
- Device memory maps
- Device pinout and packaging details
- Device electrical specifications
- List of peripherals included on the devices
THE MICROCHIP WEBSITE
Microchip provides online support via our website at www.microchip.com. This website
is used as a means to make files and information easily available to customers.
Accessible by using your favorite Internet browser, the website contains the following
information:
• Product Support – Data sheets and errata, application notes and sample
programs, design resources, user’s guides and hardware support documents,
latest software releases and archived software
• General Technical Support – Frequently Asked Questions (FAQs), technical
support requests, online discussion groups, Microchip consultant program
member listing
• Business of Microchip – Product selector and ordering guides, latest Microchip
press releases, listing of seminars and events; and listings of Microchip sales
offices, distributors and factory representatives
Preface
PRODUCT CHANGE NOTIFICATION SERVICE
Microchip’s customer notification service helps keep customers current on Microchip
products. Subscribers will receive e-mail notification whenever there are changes,
updates, revisions or errata related to a specified product family or development tool of
interest.
To register, access the Microchip website at www.microchip.com, click on Product Change Notification and follow the registration instructions.
Users of Microchip products can receive assistance through several channels:
• Distributor or Representative
• Local Sales Office
• Corporate Application Engineer (CAE)
• Embedded Solutions Engineer (ESE)
Customers should contact their distributor, representative or Embedded Solutions
Engineer (ESE) for support. Local sales offices are also available to help customers.
A listing of sales offices and locations is included in the back of this document.
Technical support is available through the website at:
http://www.microchip.com/support.
DOCUMENT REVISION HISTORY
Revision A (April 2019)
This is the initial version of this document.
DS50002853A-page 8 2019 Microchip Technology Inc.
1.1INTRODUCTION
The dsPIC33CH512MP506 Digital Power Plug-In Module (DP PIM) is a demonstration
board that, in conjunction with different power boards, showcases the Microchip
dsPIC33CH512MP506 16-Bit Digital Signal Controller (DSC) features. The DP PIM
provides access to the dsPIC33CH512MP506 analog inputs, the Digital-to-Analog
Converter (DAC) output, the Pulse-Width Modulation (PWM) outputs and the General
Purpose Input and Output (GPIO) ports.
The series of Microchip DP PIMs feature different device families, from dsPIC33E to
dsPIC33CK and dsPIC33CH. These devices have different CPU performance levels as
well as peripheral features and functions. However, even if the features and performance levels are different, all DP PIMs have the same functional card edge connector
pinout to support seamless migration between device families.
1.2FEATURES
The dsPIC33CH512MP506 DP PIM has the following features, as shown in Figure 1-1.
12. Analog input with op amp buffer via test point loop connector; can be used for
Bode plot measurements.
13. Op amp buffer for Bode input.
14. Test point loop for DAC output.
15. Test point to access RD13 (also available on card edge connector pin 12).
16. Test point to access RD15 (also available on card edge connector pin 8).
17. Op amp buffers for medium speed ADC inputs.
18. MEMS oscillator.
Board dimensions are: 51 mm (length) x 38.5 mm (width).
1.2.1Test Points
Ta bl e 1- 1 lists the test points available on the dsPIC33CH512MP506 DP PIM.
TABLE 1-1:TEST POINTS
Test Point NameFunction/Description
TP1, TP2Bode Measurement Signal Injection Point
TP3RB2_DAC1_OUT: Digital-to-Analog Converter Output
TP4Test Point for Debugging: Access to RD13 through 270 Resistor
TP5General Purpose Test Point Connected to RD15 along with LD2
(Red LED)
1.2.2Electrical Characteristics
Ta bl e 1- 2 shows the electrical characteristics of the dsPIC33CH512MP506 DP PIM.
TABLE 1-2:ELECTRICAL CHARACTERISTICS
ParameterValue
Input Voltage Range3.6 V
Current ConsumptionMinimum 82 mA, Typical 108 mA, Absolute Maximum 200 mA
Power DissipationMinimum 295 mW, Typical 414 mW, Maximum 1100 mW
Operating Temperature Range-40°C to +85°C
Note:Typical Test Conditions: Ambient Temperature +25°C, Master core running at
90 MIPS, Slave core running at 100 MIPS, all peripherals powered but not enabled,
power-on LED, LD1, active, no USB device or debugger connected.
DC to 10 VDC, Absolute Maximum 16 VDC
DS50002853A-page 10 2019 Microchip Technology Inc.
Overview
1.2.3Analog and Digital Signals
The dsPIC33CH512MP506 DP PIM ensures good signal integrity and provides all
signals needed to control a power train. These signals are divided into two main
sections: Analog and Digital.
1. Analog Section
The analog section is located at the short segment of the edge connector.
It consists of 17 signals, all referenced to the analog ground. These lines are split
into the following subsections:
• High-Speed Comparator Inputs: RC filtered with corner frequency of 10 MHz
and maximum signal rise/fall time of 33 ns. These lines are designed to be
used with on-chip comparators for signal tracking tasks, such as peak, valley
or zero-cross detections.
• High-Speed ADC Inputs: RC filtered with corner frequency of 2 MHz and
maximum signal rise/fall time of 180 ns. These lines are connected to the
Track-and-Hold (T&H) circuitry of the dedicated ADC inputs and to the
Sample-and-Hold (S&H) circuitry of the shared ADC inputs.
• Medium Speed ADC Inputs: Buffered input lines, RC filtered with corner
frequency of 1 MHz and maximum signal rise/fall time of 360 ns.
• Low-Speed ADC Inputs: RC filtered with corner frequency of 190 kHz and
maximum signal rise/fall time of 1.8 µs.
• 12-Bit DAC Output with Optional On-Board RC Filtering.
Note:RC filtering and series resistance are needed for good signal integrity, and
for reducing EMI issues. Hence, the board can be used for development
purposes under frequent plug-in/out cycles. This decoupling also increases
robustness in case of accidental shorts and EMC issues.
2. Digital Section
The digital section is located at the long segment of the edge connector.
It consists of 31 signals, all referenced to digital ground. These lines are split into
four subsections:
• High-Speed PWM Outputs: Each line has a 75 series resistance.
• Medium Speed GPIO: Each line has a 270 series resistance.
• Programing/Debugging Lines: Each line has a 100 series resistance.
• Communication Lines (SPI): Each line has a 75 series resistance.
Note:The range of the digital I/Os allows access to other peripheral functions of
the populated DSC, such as communication interfaces like I
Single-Edge Nibble Transmission (SENT), Controller Area Network (CAN),
input capture, output compare, Combinatorial Logic Cells (CLC) and more.
Please refer to the device data sheet for further information on available
functions.
The on-board USB to UART serial bridge enables easy serial connection to PCs.
The USB port can provide power to the Digital Power PIM and allows the user to
communicate with the dsPIC
The USB driver package and software tool support of the MCP2221A serial converter
also offers free terminal software for I
generic API drivers for custom software development. Please visit the MCP2221A
product web page for more details (www.microchip.com).
1.4LOW-FREQUENCY BODE PLOT MEASUREMENTS
The dsPIC33CH512MP506 device, along with an additional on-board circuitry, allows
Bode plot measurements to be performed without the need for an isolation transformer.
The transformer might still be required if the injected signal tends to be at a very low
frequency (for instance, in case of Power Factor Correction (PFC) applications).
Perform the following steps:
1. Solder the 150 resistor from position R74 to R94. Make sure that the
RD10_S1AN13_IN line is not driven by any other low-impedance source.
2. Run the power stage in Open-Loop mode with a fixed duty cycle.
3. Connect the Bode 100 AC output to TP1 and TP2. The on-board operational
amplifier will add a V
needed.
4. Connect RB2_DAC1_OUT to CH2 of the Bode 100.
5. Use the S1AN13 input to sample the signal from Bode 100 in every PWM cycle
at Frequency Switching (f
6. Remove the V
is needed).
7. Add sampled AC signal to the nominal duty cycle (PDCx) (action in firmware is
needed).
8. Use a second dedicated ADC core input (ANx) to sample the output of the plant
at FSW. The output can be:
• Output voltage.
• Average coil current sampled at T
9. Duty cycle input and plant output are converted into an analog signal using
RB2_DAC1_OUT.
The measured transfer function is the plant (power stage and digital modulator), after
scaling and ADC sampling, versus digital duty cycle input (PDCx).
DD/2 offset to regain a signal with no DC value (action in firmware
®
Digital Signal Controller (DSC).
2
C Master and Slave emulation, as well as
DD/2 (1.65V) offset. In this case, no injection transformer is
SW) (action in firmware is needed).
ON/2, where TON is the switch-on time.
Note:Due to run-time delays of Sample-and-Hold circuits and conversion time of
ADC and DAC, this measurement is only recommended for low-frequency
measurements: a maximum two decades below sampling frequency.
DS50002853A-page 12 2019 Microchip Technology Inc.
Overview
Power Stage
PWM
V
OUT
VIN
Nominal
Duty RaƟo
Output
+
Signal InjecƟŽŶ
S1AN13–
V/2
Remove Oīset
In
Bode 100
In
DAC1
Bode 100
Generator
V/2
50R
CH2
CH1
V
BODE
G = 2
VÃÖ =
V/2 + 2 x VÊ
Output
Power Stage
PWM
VOUT
V
IN
Compensator
Output
Bode 100
Generator
In
Bode 100
In
V/2
Signal
InjecƟŽn
ANx
–
V/2
Remove Oīset
Min/Max
Clamp
Reference
S1AN13
+
DAC1
50R
CH2
CH1
V
BODE
VÃÖ =
V/2 + 2 x VÊ
Output
Figure 1-2 and Figure 1-3 show examples of schemes of plant and closed-loop
R72 and R94 are alternate
places for the same resistor.
It forms an isolation switch
for Bode 100 Signal Injection.
DB2S31000L
D4
DB2S31000L
D3
DB2S31000L
D6
DB2S31000L
D5
+VDD_EXT
3.3k
0402
1%
R81
270R -> RES2134
TP LOOP Yellow
TP4
TP LOOP Yellow
TP5
A.2BOARD SCHEMATICS
Figure A-1 and Figure A-2 show the board schematics.
FIGURE A-1:dsPIC33CH512MP506 DIGITAL POWER PIM SCHEMATIC REV. 1.0 (PAGE 1 OF 2)
Board Layout and Schematics
DS50002853A-page 18 2019 Microchip Technology Inc.
Designed with
Altium.com
10k
0402
1%
R1
270R
04021%
R4
270R
04021%
R5
+3.3V +3.3V
V
DD
16
GP0
1
GP1
2
RST
3
UART RX
4
UART TX
5
GP2
6
GP3
7
SDA
8
SCL
9
V
USB
10
D-
11
D+
12
Vss
13
EP
17
NC
14
NC
15
MCP2221-I/ML
U1
4.7k
0402
1%
R6
4.7k
0402
1%
R7
SDA2
SCL2
UART TX
UART RX
GND_D
+VDD_EXT
+3.3V
GND_DGND_D
3.6V . .6 V
MAX
from Edge Connector
+5V_USB
0.1 μF
50V
0402
C8
GND_D
3.3k
0402
1%
R8
GREEN
0603
LD1
V
IN
1
SHDN
3
GND
2
PWRGD
4
V
OUT
5
MCP1755/3.3V
U2
MCLR_IN
MCLR_IN
GND_A
0R
0603
R9
GND_D
0R
0603
R10
Shield
“Shield” = Bottom copper pour connection
+3.3V_A
GND_A
+3.3V_OPA
+3.3V
GND_A
1 μF
10V
0402
C6
0.47 μF
6.3V
0402
C7
10 μF
10V
0603
C9
10 μF
10V
0603
C10
10 μF
10V
0603
C11
10 μF
10V
0603
C12
600R
0402
900 mA
FB3
600R
0402
900 mA
FB5
600R
0402
900 mA
FB6
600R
0402
900 mA
FB7
GND_U
GND_U
SBR1A20T5
D2
1 2 3 4 50
DNGV5+ -D+DDI
Micro-AB Receptacle
USB2.0 MICRO-B FEMALE
J3
GND_S
+5V_USB
USB_N
USB_P
3
1
4
2
744230900
L1
WE CNSW
1
2
3
456
82400152
D1
GND_U
USB Port
0.1 μF
50V
0402
C3
47 pF
50V
0402
C1
47 pF
50V
0402
C2
GND_UGND_UGND_U
GND_U
600R
0402
900 mA
FB4
USB/UART-I2C Interface
600R0402
900 mA
FB1
600R0402
900 mA
FB2
4.7k
0402
1%
R0
15R
0402
1%
R2
15R
0402
1%
R3
0.1 μF50V
0402
C0
5V from USB Connector
FIGURE A-2:dsPIC33CH512MP506 DIGITAL POWER PIM SCHEMATIC REV. 1.0 (PAGE 2 OF 2)
dsPIC33CH512MP506 Digital Power PIM User’s Guide
Board Layout and Schematics
Top Silkscreen
Top Copper
A.3PCB LAYOUT
The dsPIC33CH512MP506 DP PIM is a four-layer FR4, 1.55 mm, Plated-Through-Hole (PTH) PCB
construction. Figure A-3 through Figure A-5 illustrate the PCB layers and Figure A-6 shows the assembly
drawings of the dsPIC33CH512MP506 DP PIM.
FIGURE A-3:dsPIC33CH512MP506 DIGITAL POWER PIM TOP SILKSCREEN AND TOP COPPER
DS50002853A-page 26 2019 Microchip Technology Inc.
dsPIC33CH512MP506 DIGITAL
f
c
1
2 R
FiltCFilt
----------------------------------=
POWER PIM USER’S GUIDE
Appendix C. Characterization Data
This chapter provides some characterization data and further guidance on sub-circuits
of this Digital Power PIM to allow engineers to gain a better understanding of technical
limitations, as well as enable users to solve design trade-offs in additional circuits on
custom boards, such as signal conditioning or auxiliary power supplies.
Note:The graphs and tables provided following this note are a statistical
summary based on a limited number of samples and are provided for
informational purposes only. The performance characteristics listed herein
are not tested or guaranteed. In some graphs or tables, the data presented
may be outside the specified operating range (e.g., outside specified power
supply range), and therefore, outside the warranted range.
C.1MEASUREMENT ACCURACY IMPACTS
C.1.1High-Speed Analog Signal Tracking Considerations
Each of the four groups of the analog inputs, high-speed ADC, mid-speed ADC,
low-speed ADC and high-speed comparator inputs have been equipped with RC
low-pass filters to prevent corruption of sampling results, such as alias-frequencies
being injected into a series of ADC sampling results, and to ensure proper operation of
the high-speed comparators in noisy environments. These deliberate bandwidth
limitations, however, may affect the accuracy of the ADC results when tracking
high-speed signals.
C.1.1.1FILTER BANDWIDTH IMPACTS
This section discusses the influence of the RC low-pass filter bandwidth limits versus
the expected sampling error to allow designers to identify the maximum signal slew
rate, which can be tracked with a certain known accuracy.
The cutoff frequency, f
output signal magnitude is reduced by -3dB.
The first-order RC filter cutoff frequency is defined by Equation C-1.
EQUATION C-1:
When using high-speed ADCs with sampling times of 10 ns to 50 ns or less, tracking
signal transients at this frequency will also show a 3 dB offset in ADC results in
accordance to the damped signal gain. To allow a more accurate analysis of the
tracking error, with regards to the transient frequency, we need to look at the total gain
characteristic over frequency.
of an RC low-pass filter defines the frequency at which its
The transfer function of a first-order RC low-pass filter is defined by Equation C-2
through Equation C-4.
EQUATION C-2:
EQUATION C-3:
EQUATION C-4:
FIGURE C-1:FIRST-ORDER RC LOW-PASS FILTER TRANSFER FUNCTION
DS50002853A-page 28 2019 Microchip Technology Inc.
By plotting the frequency domain transfer function of the RC filter, it is shown that the
output voltage of the RC filter network at the cutoff frequency, f
amplitude, but also shifted in time. While the amplitude reduction is absolute, the phase
delay may require a relocation of the ADC sample trigger to achieve accurate results.
As both magnitude and phase of the RC filter output signal do not change instantly, but
over frequency with varying degree, the deviation from the unfiltered feedback signal,
and thus, the related ADC result deviation, may have to be considered.
, is not only damped in
c
Characterization Data
C.1.2Example
In order to demonstrate the impact of the on-board RC filtering, the following example
shows the impact when tracking the average value of a 500 kHz at 50% duty cycle
current feedback signal with minimum sampling error.
Let the average value be 500 mV and the peak-to-peak voltage 200 mV, following ideal
current-to-voltage conversion. Figure C-2 shows the unfiltered ideal signal along with
the waveforms obtained after this signal is passed through any of the on-board RC
filters. Note that the filtering does not alter the average value along (ADC Input
Voltage = 0.5) any of the filtered signals. The mid-points of each filtered AC signals,
however, have been shifted in time with respect to the phase delay of the RC filter.
When this phase delay is not properly considered, the ADC trigger may be displaced
from the desired average point of the oversampled signal, resulting in a significant
measurement error.
FIGURE C-2:UNFILTERED AND FILTERED TRIANGULAR WAVEFORMS
Depending on the application, in order to obtain the average value with the required
accuracy, a time delay in the sampling trigger of the ADC might need to be introduced.
In our specific case, in order to take the sample with the best accuracy, the trigger
should be offset by approximately 60, 135 and 390 ns, as shown in Figure C-3.
FIGURE C-3:SAMPLING TRIGGER PLACEMENT FOR BEST ACCURACY
C.1.2.1STEP RESPONSE DELAY ESTIMATION
Deriving from Equation C-1, the time constant of the first-order RC filter is defined by
Equation C-5, which is generally used to characterize the response of a first-order RC
filter to a step input, as shown in Equation C-6.
EQUATION C-5:
EQUATION C-6:
DS50002853A-page 30 2019 Microchip Technology Inc.
Figure C-4 shows the calculated step responses of the on-board filters normalized to
t100
V
OUT
t VINt–
VINt
----------------------------------------
=
t100 e
t–
=
the input voltage.
FIGURE C-4:NORMALIZED STEP RESPONSE
Characterization Data
In case a sample is taken at the filter output time, t, after the step input was applied, the
percentage error with respect to the settled value can be calculated by using
Equation C-7 and Equation C-8 (substituting Equation C-6).
Figure C-5 depicts the remaining percentage error with respect to the sampling time.
FIGURE C-5:NORMALIZED OUTPUT ERROR
On the other hand, if a maximum tolerable percentage error,
advance, the earliest time the sample should be taken can be calculated by using
Equation C-9, which is obtained from Equation C-8 by expressing t.
EQUATION C-9:
Filter capacitors on the board are either 560 pF or 5600 pF, whereas the on-chip hold
capacitance is around 5 pF. Due to the large ratio of the on-board versus on-chip
capacities, and for the sake of simplicity, the loading effect of the Sample-and-Hold
(S&H) circuitry has been neglected here.
, is defined in
max
DS50002853A-page 32 2019 Microchip Technology Inc.
PIN value depends on the device package and is not tested. The effect of
the C
PIN is negligible if RS5 k.
Demanding applications, however, might need to consider the loading effect of the S&H
capacitance as well. The electrical model shown in Figure C-6 can be used to make
more elaborate calculations.