Rainbow Electronics MAX188 User Manual

19-0123; Rev. 4; 8/96
EVALUATION KIT
AVAILABLE
_______________General Description
The MAX186/MAX188 are 12-bit data-acquisition sys­tems that combine an 8-channel multiplexer, high-band­width track/hold, and serial interface together with high conversion speed and ultra-low power consumption. The devices operate with a single +5V supply or dual ±5V supplies. The analog inputs are software config­urable for unipolar/bipolar and single-ended/differential operation.
The 4-wire serial interface directly connects to SPI™, QSPI™ and Microwire™ devices without external logic. A serial strobe output allows direct connection to TMS320 family digital signal processors. The MAX186/MAX188 use either the internal clock or an external serial-interface clock to perform successive-approximation A/D conver­sions. The serial interface can operate beyond 4MHz when the internal clock is used.
The MAX186 has an internal 4.096V reference while the MAX188 requires an external reference. Both parts have a reference-buffer amplifier that simplifies gain trim .
The MAX186/MAX188 provide a hard-wired SHDN pin and two software-selectable power-down modes. Accessing the serial interface automatically powers up the devices, and the quick turn-on time allows the MAX186/MAX188 to be shut down between every conversion. Using this technique of powering down between conversions, supply current can be cut to under 10µA at reduced sampling rates.
The MAX186/MAX188 are available in 20-pin DIP and SO packages, and in a shrink small-outline package (SSOP), that occupies 30% less area than an 8-pin DIP. For applications that call for a parallel interface, see the MAX180/MAX181 data sheet. For anti-aliasing filters, consult the MAX274/MAX275 data sheet.
________________________Applications
Portable Data Logging Data-Acquisition High-Accuracy Process Control Automatic Testing Robotics Battery-Powered Instruments Medical Instruments
SPI and QSPI are registered trademarks of Motorola. Microwire is a registered trademark of National Semiconductor.
Low-Power, 8-Channel,
Serial 12-Bit ADCs
____________________________Features
8-Channel Single-Ended or 4-Channel
Differential Inputs
Single +5V or ±5V OperationLow Power: 1.5mA (operating mode)
2µA (power-down mode)
Internal Track/Hold, 133kHz Sampling RateInternal 4.096V Reference (MAX186)SPI-, QSPI-, Microwire-, TMS320-Compatible
4-Wire Serial Interface
Software-Configurable Unipolar or Bipolar Inputs20-Pin DIP, SO, SSOP PackagesEvaluation Kit Available
______________Ordering Information
PART
MAX186_CPP 20 Plastic DIP MAX186_CWP 20 SO MAX186_CAP MAX186DC/D Dice* MAX186_EPP 20 Plastic DIP MAX186_EWP 20 SO MAX186_EAP -40°C to +85°C 20 SSOP MAX186_MJP -55°C to +125°C 20 CERDIP**
Ordering Information continued on last page.
NOTE: Parts are offered in grades A, B, C and D (grades defined in Electrical Characteristics). When ordering, please specify grade. Contact factory for availability of A-grade in SSOP package. * Dice are specified at +25°C, DC parameters only. * * Contact factory for availability and processing to MIL-STD-883.
____________________Pin Configuration
TOP VIEW
TEMP. RANGE
0°C to +70°C 0°C to +70°C 0°C to +70°C 0°C to +70°C
-40°C to +85°C
-40°C to +85°C
CH0
1 2
CH1
3
CH2 CH3
4 5
CH4
6
CH5 CH6
7 8
CH7
9
V
SS
10
DIP/SO/SSOP
MAX186 MAX188
PIN-PACKAGE
20 SSOP
V
20
DD
SCLK
19
CS
18 17
DIN
16
SSTRB DOUT
15
DGND
14 13
AGND
12
REFADJ
11
VREFSHDN
MAX186/MAX188
________________________________________________________________ Maxim Integrated Products
1
For free samples & the latest literature: http://www.maxim-ic.com, or phone 1-800-998-8800
Low-Power, 8-Channel, Serial 12-Bit ADCs
ABSOLUTE MAXIMUM RATINGS
VDDto AGND............................................................-0.3V to +6V
VSSto AGND............................................................+0.3V to -6V
VDDto VSS..............................................................-0.3V to +12V
AGND to DGND.....................................................-0.3V to +0.3V
CH0–CH7 to AGND, DGND.............(VSS- 0.3V) to (VDD+ 0.3V)
CH0–CH7 Total Input Current ..........................................±20mA
VREF to AGND ...........................................-0.3V to (VDD+ 0.3V)
REFADJ to AGND.......................................-0.3V to (VDD+ 0.3V)
Digital Inputs to DGND...............................-0.3V to (VDD+ 0.3V)
Digital Outputs to DGND............................-0.3V to (VDD+ 0.3V)
Digital Output Sink Current.................................................25mA
Stresses beyond those listed under “Absolute Maximum Ratings” may cause permanent damage to the device. These are stress ratings only, and functional operation of the device at these or any other conditions beyond those indicated in the operational sections of the specifications is not implied. Exposure to absolute maximum rating conditions for extended periods may affect device reliability.
ELECTRICAL CHARACTERISTICS
MAX186/MAX188
(VDD= 5V ±5%; VSS= 0V or -5V; f
4.7µF capacitor at VREF pin; MAX188—external reference, VREF = 4.096V applied to VREF pin; T noted.)
PARAMETER SYMBOL MIN TYP MAX UNITS
DC ACCURACY (Note 1)
Resolution 12 Bits
Relative Accuracy (Note 2)
Differential Nonlinearity DNL ±1 LSB
Offset Error
Gain Error (Note 3)
Gain Temperature Coefficient ±0.8 ppm/°C Channel-to-Channel
Offset Matching DYNAMIC SPECIFICATIONS (10kHz sine wave input, 4.096V Signal-to-Noise + Distortion Ratio Total Harmonic Distortion
(up to the 5th harmonic) Spurious-Free Dynamic Range SFDR 80 dB Channel-to-Channel Crosstalk -85 dB
= 2.0MHz, external clock (50% duty cycle); 15 clocks/conversion cycle (133ksps); MAX186—
CLK
MAX186A/MAX188A MAX186B/MAX188B MAX186C MAX188C MAX186D/MAX188D No missing codes over temperature MAX186A/MAX188A MAX186B/MAX188B MAX186C/MAX188C MAX186D/MAX188D MAX186 (all grades)
External reference
4.096V (MAX188)
External reference, 4.096V
SINAD 70 dB
THD -80 dB
65kHz, VIN= 4.096V
Continuous Power Dissipation (TA= +70°C)
Plastic DIP (derate 11.11mW/°C above +70°C) ...........889mW
SO (derate 10.00mW/°C above +70°C)........................800mW
SSOP (derate 8.00mW/°C above +70°C) .....................640mW
CERDIP (derate 11.11mW/°C above +70°C)................889mW
Operating Temperature Ranges:
MAX186_C/MAX188_C........................................0°C to +70°C
MAX186_E/MAX188_E......................................-40°C to +85°C
MAX186_M/MAX188_M..................................-55°C to +125°C
Storage Temperature Range.............................-60°C to +150°C
Lead Temperature (soldering, 10sec).............................+300°C
= T
to T
A
MIN
CONDITIONS
MAX188A MAX188B MAX188C MAX188D
±0.1 LSB
, 133ksps, 2.0MHz external clock, bipolar input mode)
P-P
(Note 4)
P-P
, unless otherwise
MAX
±0.5 ±0.5 ±1.0
±0.75
±1.0
±2.0 ±3.0 ±3.0 ±3.0 ±3.0 ±1.5 ±2.0 ±2.0 ±3.0
LSB
LSB
LSB
2 _______________________________________________________________________________________
Low-Power, 8-Channel,
Serial 12-Bit ADCs
ELECTRICAL CHARACTERISTICS (continued)
(VDD= 5V ±5%; VSS= 0V or -5V; f
4.7µF capacitor at VREF pin; MAX188—external reference, VREF = 4.096V applied to VREF pin; T noted.)
PARAMETER SYMBOL CONDITIONS MIN TYP MAX UNITS
Small-Signal Bandwidth -3dB rolloff 4.5 MHz Full-Power Bandwidth 800 kHz
CONVERSION RATE
Conversion Time (Note 5) t Track/Hold Acquisition Time t
Aperture Delay 10 ns Aperture Jitter <50 ps Internal Clock Frequency 1.7 MHz
External Clock Frequency Range
ANALOG INPUT
Input Voltage Range, Single-Ended and Differential (Note 9)
Multiplexer Leakage Current Input Capacitance (Note 6) 16 pF
INTERNAL REFERENCE (MAX186 only, reference buffer enabled) VREF Output Voltage VREF Short-Circuit Current 30 mA
VREF Tempco
Load Regulation (Note 7) 0mA to 0.5mA output load 2.5 mV Capacitive Bypass at VREF
Capacitive Bypass at REFADJ REFADJ Adjustment Range ±1.5 %
EXTERNAL REFERENCE AT VREF (Buffer disabled, VREF = 4.096V) Input Voltage Range V Input Current 200 350 µA
Input Resistance 12 20 k Shutdown VREF Input Current 1.5 10 µA
Buffer Disable Threshold REFADJ
= 2.0MHz, external clock (50% duty cycle); 15 clocks/conversion cycle (133ksps); MAX186—
CLK
CONV
AZ
Internal clock 5.5 10 External clock, 2MHz, 12 clocks/conversion 6
External compensation, 4.7µF Internal compensation (Note 6) 0.1 0.4 Used for data transfer only 10
Unipolar, VSS= 0V
Bipolar, VSS= -5V On/off leakage current, VIN= ±5V
TA= +25°C
MAX186A, MAX186B, MAX186C
MAX186D ±30
Internal compensation 0 External compensation 4.7 Internal compensation 0.01 External compensation 0.01
MAX186_C MAX186_E MAX186_M
= T
to T
A
MIN
0.1 2.0
±0.01 ±1 µA
4.076 4.096 4.116 V
±30 ±50 ±30 ±60 ±30 ±80
2.50
VDD­50mV
, unless otherwise
MAX
1.5 µs
0 to
VREF
±VREF/2
V
DD
+
50mV
ppm/°C
MAX186/MAX188
µs
MHz
V
µF
µF
V
_______________________________________________________________________________________ 3
Low-Power, 8-Channel,
SHDN
Serial 12-Bit ADCs
ELECTRICAL CHARACTERISTICS (continued)
(VDD= 5V ±5%; VSS= 0V or -5V; f
4.7µF capacitor at VREF pin; MAX188—external reference, VREF = 4.096V applied to VREF pin; T noted.)
PARAMETER
EXTERNAL REFERENCE AT REFADJ
Reference-Buffer Gain
DIGITAL INPUTS (DIN, SCLK, CS,
DIN, SCLK, CS Input High Voltage
MAX186/MAX188
DIN, SCLK, CS Input Low Voltage DIN, SCLK, CS Input Hysteresis DIN, SCLK, CS Input Leakage DIN, SCLK, CS Input Capacitance
SHDN Input High Voltage SHDN Input Low Voltage SHDN Input Current, High SHDN Input Current, Low SHDN Input Mid Voltage SHDN Voltage, Floating SHDN Max Allowed Leakage,
Mid Input
DIGITAL OUTPUTS (DOUT, SSTRB)
Output Voltage Low V Output Voltage High V
Three-State Leakage Current I Three-State Output Capacitance C
POWER REQUIREMENTS
Positive Supply Voltage V Negative Supply Voltage V
Positive Supply Current I
Negative Supply Current I
= 2.0MHz, external clock (50% duty cycle); 15 clocks/conversion cycle (133ksps); MAX186—
CLK
SYMBOL CONDITIONS MIN TYP MAX
Internal compensation mode 0 External compensation mode 4.7 MAX186 1.678 MAX188 1.638 MAX186 ±50 MAX188 ±5
)
V
INH
V
INL
V
HYST
C V V
I
I
V V
I
INH
INL INH INL
FLT
OH
OUT
DD
DD
SS
VIN= 0V or V
IN
(Note 6) 15 pF
IN
SHDN = V SHDN = 0V
IM
SHDN = open SHDN = open
I
OL
SS
SINK
I
SINK
I
SOURCE
CS = 5V
L
CS = 5V (Note 6)
Operating mode 1.5 2.5 Fast power-down 30 70 Full power-down 210 Operating mode and fast power-down 50 Full power-down 10
DD
DD
= 5mA 0.4 = 16mA 0.3
= 1mA 4 V
= T
to T
A
MIN
2.4 V
0.15 V
VDD- 0.5 V
-4.0 µA
1.5 VDD-1.5
2.75 V
-100 100 nA
5 ±5% V
0 or
-5 ±5%
, unless otherwise
MAX
0.8 V
±1 µA
0.5 V
4.0 µA
±10 µA
15 pF
UNITS
V/V
mA
µFCapacitive Bypass at VREF
µAREFADJ Input Current
V
V
V
µA
µA
4 _______________________________________________________________________________________
Low-Power, 8-Channel,
Serial 12-Bit ADCs
ELECTRICAL CHARACTERISTICS (continued)
(VDD= 5V ±5%; VSS= 0V or -5V; f
4.7µF capacitor at VREF pin; MAX188—external reference, VREF = 4.096V applied to VREF pin; T noted.)
PARAMETER SYMBOL CONDITIONS UNITS
Positive Supply Rejection (Note 8)
Negative Supply Rejection (Note 8)
Note 1: Tested at VDD= 5.0V; VSS= 0V; unipolar input mode. Note 2: Relative accuracy is the deviation of the analog value at any code from its theoretical value after the full-scale range has
been calibrated.
Note 3: MAX186 – internal reference, offset nulled; MAX188 – external reference (VREF = +4.096V), offset nulled. Note 4: Ground on-channel; sine wave applied to all off channels. Note 5: Conversion time defined as the number of clock cycles times the clock period; clock has 50% duty cycle. Note 6: Guaranteed by design. Not subject to production testing. Note 7: External load should not change during conversion for specified accuracy. Note 8: Measured at V
SUPPLY
+5% and V
Note 9: The common-mode range for the analog inputs is from V
= 2.0MHz, external clock (50% duty cycle); 15 clocks/conversion cycle (133ksps); MAX186—
CLK
= T
to T
A
MIN
, unless otherwise
MAX
MIN TYP MAX
PSR ±0.06 ±0.5 mV
PSR
VDD= 5V ±5%; external reference, 4.096V; full-scale input
VSS= -5V ±5%; external reference, 4.096V; full-scale input
-5% only.
SUPPLY
SS
to VDD.
±0.01 ±0.5 mV
TIMING CHARACTERISTICS
(VDD= 5V ±5%; V
=0V or -5V, TA= T
SS
MIN
to T
, unless otherwise noted.)
MAX
MAX186/MAX188
PARAMETER SYMBOL CONDITIONS UNITS
Acquisition Time DIN to SCLK Setup DIN to SCLK Hold
SCLK Fall to Output Data Valid
CS Fall to Output Enable CS Rise to Output Disable CS to SCLK Rise Setup CS to SCLK Rise Hold
SCLK Pulse Width High SCLK Pulse Width Low SCLK Fall to SSTRB CS Fall to SSTRB Output Enable
(Note 6) CS Rise to SSTRB Output Disable
(Note 6) SSTRB Rise to SCLK Rise
(Note 6)
_______________________________________________________________________________________ 5
t
AZ
t
DS
t
DH
t
DO
t
DV
t
TR
t
CSS
t
CSH
t
CH
t
CL
t
SSTRB
t
SDV
t
STR
t
SCK
MIN TYP MAX
1.5 µs
100 ns
0 ns C C
C
LOAD
LOAD LOAD
= 100pF = 100pF
= 100pF
MAX18_ _C/E MAX18_ _M
20 150 ns 20 200 ns
100 ns 100 ns
100 ns
0 ns 200 ns 200 ns
C
= 100pF
LOAD
External clock mode only, C
External clock mode only, C
LOAD
LOAD
= 100pF
= 100pF
200 ns 200 ns
200 ns
Internal clock mode only 0 ns
Low-Power, 8-Channel, Serial 12-Bit ADCs
__________________________________________Typical Operating Characteristics
POWER-SUPPLY REJECTION
vs. TEMPERATURE
0.30
0.25
0.20
0.15
0.10
PSR (LSBs)
0.05
0.00
MAX186/MAX188
-0.05
-60 140
-20 0 40 80 120
-40 20 100 TEMPERATURE (°C)
VDD = +5V ±5% VSS = 0V or -5V
60
20
0
-20
-40
-60
INTERNAL REFERENCE VOLTAGE
vs. TEMPERATURE
2.456
2.455
2.454
VREFADJ (V)
2.453
2.452
-40 -20 0 20 40 60 80 100 120 TEMPERATURE (°C)
MAX186/MAX188 FFT PLOT – 133kHz
ft = 10kHz fs = 133kHz
ft = 10kHz
= 133kHz
f
s
= +25°C
T
A
CHANNEL-TO-CHANNEL OFFSET MATCHING
vs. TEMPERATURE
0.16
0.14
0.12
0.10
0.08
0.06
0.04
OFFSET MATCHING (LSBs)
0.02 0
-60 -20 60 140
-40 0 40 80 120
20 100
TEMPERATURE (°C)
-80
AMPLITUDE (dB)
-100
-120
-140 0

  
FREQUENCY
33.25kHz
66.5kHz
_____________________________________________________________Pin Description
PIN NAME FUNCTION
1-8 CH0-CH7 Sampling Analog Inputs
9
10
11 VREF
6
________________________________________________________________________________________________
V
SS
SHDN
Negative Supply Voltage. Tie to -5V ±5% or AGND Three-Level Shutdown Input. Pulling SHDN low shuts the MAX186/MAX188 down to 10µA (max)
supply current, otherwise the MAX186/MAX188 are fully operational. Pulling SHDN high puts the ref­erence-buffer amplifier in internal compensation mode. Letting SHDN float puts the reference-buffer amplifier in external compensation mode.
Reference Voltage for analog-to-digital conversion. Also, Output of the Reference Buffer Amplifier (4.096V in the MAX186, 1.638 x REFADJ in the MAX188). Add a 4.7µF capacitor to ground when using external compensation mode. Also functions as an input when used with a precision external reference.
Low-Power, 8-Channel,
Serial 12-Bit ADCs
________________________________________________Pin Description (continued)
PIN NAME FUNCTION
12 REFADJ
13 AGND Analog Ground. Also IN- Input for single-ended conversions. 14 DGND 15 DOUT
16 SSTRB
17 DIN
18
CS
19 SCLK
20
V
DD
Input to the Reference-Buffer Amplifier. To disable the reference-buffer amplifier, tie REFADJ to V
.
DD
Digital Ground Serial Data Output. Data is clocked out at the falling edge of SCLK. High impedance when CS is high.
Serial Strobe Output. In internal clock mode, SSTRB goes low when the MAX186/MAX188 begin the A/D conversion and goes high when the conversion is done. In external clock mode, SSTRB pulses high for one clock period before the MSB decision. High impedance whenCS is high (external mode).
Serial Data Input. Data is clocked in at the rising edge of SCLK. Active-Low Chip Select. Data will not be clocked into DIN unless CS is low. When CS is high, DOUT
is high impedance. Serial Clock Input. Clocks data in and out of serial interface. In external clock mode, SCLK also sets
the conversion speed. (Duty cycle must be 40% to 60% in external clock mode.) Positive Supply Voltage, +5V ±5%
+5V
MAX186/MAX188
DOUT
3k
a. High-Z to V
DGND
and VOL to V
OH
C
LOAD
OH
DOUT
b. High-Z to VOL and VOH to V
Figure 1. Load Circuits for Enable Time
DOUT
3k
DGND
a VOH to High-Z b VOL to High-Z
C
DOUT
LOAD
Figure 2. Load Circuits for Disabled Time
+5V
3k
C
LOAD
DGND
3k
C
LOAD
DGND
18
CS
19
SCLK
DIN
SHDN
OL
CH0 CH1 CH2
CH3 CH4
CH5 CH6 CH7
AGND
REFADJ
VREF
SHIFT
REGISTER
10
1 2 3
4
ANALOG
INPUT
5
MUX
6
7 8
13
12 11
CONTROL
+2.46V
REFERENCE
(MAX186)
LOGIC
T/H
20k
INPUT
17
CLOCK
IN
A
1.65
+4.096V
INT
CLOCK
12-BIT
SAR ADC
REF
OUTPUT
REGISTER
OUT
MAX186 MAX188
SHIFT
15
DOUT
16
SSTRB
20
V
DD
14
DGND
9
V
SS
Figure 3. Block Diagram
_______________________________________________________________________________________ 7
Low-Power, 8-Channel, Serial 12-Bit ADCs
_______________Detailed Description
The MAX186/MAX188 use a successive-approximation conversion technique and input track/hold (T/H) circuit­ry to convert an analog signal to a 12-bit digital output. A flexible serial interface provides easy interface to microprocessors. No external hold capacitors are required. Figure 3 shows the block diagram for the MAX186/MAX188.
Pseudo-Differential Input
The sampling architecture of the ADC’s analog com­parator is illustrated in the Equivalent Input Circuit (Figure 4). In single-ended mode, IN+ is internally switched to CH0-CH7 and IN- is switched to AGND. In differential mode, IN+ and IN- are selected from pairs of CH0/CH1, CH2/CH3, CH4/CH5 and CH6/CH7.
MAX186/MAX188
Configure the channels with Table 3 and Table 4. In differential mode, IN- and IN+ are internally switched
to either one of the analog inputs. This configuration is pseudo-differential to the effect that only the signal at IN+ is sampled. The return side (IN-) must remain sta­ble within ±0.5LSB (±0.1LSB for best results) with respect to AGND during a conversion. Accomplish this by connecting a 0.1µF capacitor from AIN- (the select­ed analog input, respectively) to AGND.
During the acquisition interval, the channel selected as the positive input (IN+) charges capacitor C acquisition interval spans three SCLK cycles and ends on the falling SCLK edge after the last bit of the input control word has been entered. At the end of the acqui­sition interval, the T/H switch opens, retaining charge on C
as a sample of the signal at IN+.
HOLD
The conversion interval begins with the input multiplex­er switching C
from the positive input (IN+) to the
HOLD
negative input (IN-). In single-ended mode, IN- is sim­ply AGND. This unbalances node ZERO at the input of the comparator. The capacitive DAC adjusts during the remainder of the conversion cycle to restore node ZERO to 0V within the limits of 12-bit resolution. This action is equivalent to transferring a charge of 16pF x
+) - (VIN-)] from C
[(V
IN
to the binary-weighted
HOLD
capacitive DAC, which in turn forms a digital represen­tation of the analog input signal.
The T/H enters its tracking mode on the falling clock edge after the fifth bit of the 8-bit control word has been shifted in. The T/H enters its hold mode on the falling clock edge after the eighth bit of the control word has been shifted in. If the converter is set up for
HOLD
Track/Hold
. The
12-BIT CAPACITIVE DAC
VREF
C
INPUT
CH0 CH1
CH2 CH3 CH4 CH5 CH6 CH7
AGND SINGLE-ENDED MODE: IN+ = CHO-CH7, IN– = AGND.
DIFFERENTIAL MODE: IN+ AND IN– SELECTED FROM PAIRS OF  CH0/CH1, CH2/CH3, CH4/CH5, CH6/CH7.
Figure 4. Equivalent Input Circuit
MUX
C
SWITCH
HOLD
16pF
TRACK
+
T/H
SWITCH
10k R
S
COMPARATOR
ZERO
HOLD
AT THE SAMPLING INSTANT, THE MUX INPUT SWITCHES  FROM THE SELECTED IN+  CHANNEL TO THE SELECTED  IN– CHANNEL.
single-ended inputs, IN- is connected to AGND, and the converter samples the “+” input. If the converter is set up for differential inputs, IN- connects to the “-” input, and the difference of
|IN+ - IN-| is sampled. At
the end of the conversion, the positive input connects back to IN+, and C
charges to the input signal.
HOLD
The time required for the T/H to acquire an input signal is a function of how quickly its input capacitance is charged. If the input signal’s source impedance is high, the acquisition time lengthens and more time must be allowed between conversions. Acquisition time is cal­culated by:
= 9 x (RS+ RIN) x 16pF,
t
AZ
where R input signal, and t
= 5k, RS= the source impedance of the
IN
is never less than 1.5µs. Note that
AZ
source impedances below 5kdo not significantly affect the AC performance of the ADC. Higher source impedances can be used if an input capacitor is con­nected to the analog inputs, as shown in Figure 5. Note that the input capacitor forms an RC filter with the input source impedance, limiting the ADC’s signal bandwidth.
Input Bandwidth
The ADC’s input tracking circuitry has a 4.5MHz small-signal bandwidth, so it is possible to digitize high-speed transient events and measure periodic sig­nals with bandwidths exceeding the ADC’s sampling rate by using undersampling techniques. To avoid high-frequency signals being aliased into the frequency band of interest, anti-alias filtering is recommended.
8 _______________________________________________________________________________________
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