K4H641638Q-LCCCT - Samsung Semiconductor Division

- 1 -

K4H641638Q

Rev. 1.1, Sep. 2010

SAMSUNG ELECTRONICS RESERVES THE RIGHT TO CHANGE PRODUCTS, INFORMATION AND

SPECIFICATIONS WITHOUT NOTICE.

Products and specifications discussed herein are for reference purposes only. All information discussed

herein is provided on an "AS IS" basis, without warranties of any kind.

This document and all information discussed herein remain the sole and exclusive property of Samsung

Electronics. No license of any patent, copyright, mask work, trademark or any other intellectual property

right is granted by one party to the other party under this document, by implication, estoppel or other-

wise.

Samsung products are not intended for use in life support, critical care, medical, safety equipment, or

similar applications where product failure could result in loss of life or personal or physical harm, or any

military or defense application, or any governmental procurement to which special terms or provisions

may apply.

For updates or additional information about Samsung products, contact your nearest Samsung office.

All brand names, trademarks and registered trademarks belong to their respective owners.

64Mb Q-die DDR SDRAM

66TSOP-(II) with Lead-Free & Halogen-Free

(RoHS compliant)

datasheet

- 2 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

Revision History

Revision No. History Draft Date Remark Editor

1.0 - First Spec. Release May. 2010 - S.H.Kim

1.1 - Added EMRS Table on page 21. Sep. 2010 - S.H.Kim

- 3 -
K4H641638Q datasheet DDR  SDRAM
Rev. 1.1
Table Of Contents
64Mb Q-die DDR SDRAM
Key Features................................................................................................................................................................. 4
Ordering Information ..................................................................................................................................................... 4
Operating Frequencies ................................................................................................................................................. 4
Pin / Ball Description..................................................................................................................................................... 5
Package Physical Dimension........................................................................................................................................ 6
Block Diagram (1Mb x16 I/O x4 Banks)........................................................................................................................ 7
Input/Output Function Description ................................................................................................................................ 8
Command Truth Table .................................................................................................................................................. 9
General Description ...................................................................................................................................................... 10
Absolute Maximum Rating .......................................................................................................................................... 10
DC Operating Conditions ............................................................................................................................................ 10
DDR SDRAM Spec Items & Test Conditions.............................................................................................................. 11
Input/Output Capacitance ........................................................................................................................................... 11
Detailed test condition for DDR SDRAM IDD1 & IDD7A ............................................................................................ 12
DDR SDRAM IDD Spec Table.................................................................................................................................... 13
AC Operating Conditions ............................................................................................................................................ 14
AC Overshoot/Undershoot specification for Address and Control Pins ...................................................................... 14
Overshoot/Undershoot specification for Data, Strobe and Mask Pins ........................................................................ 15
AC Timing Parameters & Specifications ..................................................................................................................... 16
System Characteristics for DDR SDRAM ................................................................................................................... 17
Component Notes ....................................................................................................................................................... 18
System Notes.............................................................................................................................................................. 20
Output Drive Strength and Extended Mode Register Set for 64Mb DDR ................................................................... 21
IBIS : I/V Characteristics for Input and Output Buffers................................................................................................ 22

- 4 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

1. Key Features

• VDD : 2.5V ± 0.2V, VDDQ : 2.5V ± 0.2V for 400

• Double-data-rate architecture; two data transfers per clock cycle

• Bidirectional data strobe [DQS] (x4,x8) & [L(U)DQS] (x16)

• Four banks operation

• Differential clock inputs(CK and CK)

• DLL aligns DQ and DQS transition with CK transition

• MRS cycle with address key programs

-. Read latency : DDR400(3 Clock)

-. Burst length (2, 4, 8)

-. Burst type (sequential & interleave)

• All inputs except data & DM are sampled at the positive going edge of the system clock(CK)

• Data I/O transactions on both edges of data strobe

• Edge aligned data output, center aligned data input

• LDM,UDM for write masking only (x16)

• DM for write masking only (x4, x8)

• Auto & Self refresh

• 15.6us refresh interval(4K/64ms refresh)

• Maximum burst refresh cycle : 8

• 66pin TSOP II Lead-Free and Halogen-Free package

• RoHS compliant

2. Ordering Information

NOTE :

1. “L” Part number(12th digit) stands for RoHS compliant and Halogen-Free product.

3. Operating Frequencies

Part No. Org. Max Freq. Interface Package NOTE

K4H641638Q-LC/LCC 4M x 16 CC(DDR400@CL=3) SSTL2 66pin TSOP II

Lead-Free & Halogen-Free 1

CC(DDR400@CL=3)

Speed @CL2 -

Speed @CL2.5 166MHz

Speed @CL3 200MHz

CL-tRCD-tRP 3-3-3

- 5 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

4. Pin / Ball Description

DM is internally loaded to match DQ and DQS identically.

Row & Column address configuration

Organization Row Address Column Address

4Mx16 A0~A11 A0-A7

64Mb TSOP-II Package Pinout

66Pin TSOP

(400mil x 875mil)

(0.65mm Pin Pitch)

Bank Address

BA0~BA1

Auto Precharge

A10

DDQ

SSQ

DDQ

SSQ

RAS

CAS

LDM

DDQ

AP/A

LDQS

SSQ

DDQ

SSQ

DDQ

CKE

UDM

REF

SSQ

UDQS

4Mb x 16

66pin TSOP - II

- 6 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

5. Package Physical Dimension

66Pin TSOP(II) Package Dimension

(1.50)

#66 #34

#33

10.16 ± 0.10

(R 0.15)

22.22 ± 0.10

0.210 ± 0.05

0.665 ± 0.05

(R 0.15)

(0.71) [0.65 ± 0.08]

0.65TYP

0.30

(10°)

(10.76)

0.125 +0.075

- 0.035

(10°)

11.76 ± 0.20

(0.80)

(0.50)

(4°)

0.45 ~ 0.75

(0° ∼ 8°)

0.25TYP

(R 0.25)

± 0.08

1.00 ± 0.10

0.05 MIN

1.20 MAX

0.10 MAX

0.075 MAX

[

NOTE

1. ( ) IS REFERENCE

2. [ ] IS ASS’Y OUT QUALITY

Detail A Detail B

Detail BDetail A

0.25 ± 0.08

Unit : mm

- 7 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

6. Block Diagram (1Mb x16 I/O x4 Banks)

Bank Select

Timing Register

Address Register

Refresh Counter

Row Buffer

Row Decoder Col. Buffer

Data Input Register

Serial to parallel

0.5Mx32

Sense AMP

2-bit prefetch

Output BufferI/O Control

Column Decoder

Latency & Burst Length

Programming Register

DLL

Strobe

Gen.

CK, CK

ADD

LCKE

CK, CK CKE CS RAS CAS WE

CK, CK

LCAS

LRAS LCBR LWE

LWCBR

LRAS

LCBR

CK, CK

x8/16/32

32 16

x4/8/16 LWE

DQi

Data Strobe

LUDM (x16)

DM Input Register

LUDM (x16)

- 8 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

7. Input/Output Function Description

SYMBOL TYPE DESCRIPTION

CK, CK Input

Clock : CK and CK are differential clock inputs. All address and control input signals are sampled on the

positive edge of CK and negative edge of CK. Output (read) data is referenced to both edges of CK. Inter-

nal clock signals are derived from CK/CK.

CKE Input

Clock Enable : CKE HIGH activates, and CKE LOW deactivates internal clock signals, and device input buf-

fers and output drivers. Taking CKE Low provides PRECHARGE POWER-DOWN and SELF REFRESH

operation (all banks idle), or ACTIVE POWER-DOWN (row ACTIVE in any bank). CKE is synchronous for

POWER-DOWN entry and exit, and for SELF REFRESH entry. CKE is asynchronous for SELF REFRESH

exit, and for output disable. CKE must be maintained high throughput READ and WRITE accesses. Input

buffers, excluding CK, CK and CKE are disabled during POWER-DOWN. Input buffers, excluding CKE are

disabled during SELF REFRESH. CKE is an SSTL_2 input, but will detect an LVCMOS Low level after VDD

is applied upon 1st power up, After VREF has become stable during the power on and initialization

sequence, it must be maintained for proper operation of the CKE receiver. For proper SELF-REFRESH

entry and exit, VREF must be maintained to this input.

CS Input

Chip Select : CS enables(registered LOW) and disables(registered HIGH) the command decoder. All com-

mands are masked when CS is registered HIGH. CS provides for external bank selection on systems with

multiple banks. CS is considered part of the command code.

RAS, CAS, WE Input Command Inputs : RAS, CAS and WE (along with CS) define the command being entered.

LDM,(UDM) Input

Input Data Mask : DM is an input mask signal for write data. Input data is masked when DM is sampled

HIGH along with that input data during a WRITE access. DM is sampled on both edges of DQS. Although

DM pins are input only, the DM loading matches the DQ and DQS loading. For the x16, LDM corresponds

to the data on DQ0~D7 ; UDM corresponds to the data on DQ8~DQ15. DM may be driven high, low, or

floating during READs.

BA0, BA1 Input Bank Addres Inputs : BA0 and BA1 define to which bank an ACTIVE, READ, WRITE or PRECHARGE

command is being applied.

A [0 : 11] Input

Address Inputs : Provide the row address for ACTIVE commands, and the column address and AUTO

PRECHARGE bit for READ/WRITE commands, to select one location out of the memory array in the

respective bank. A10 is sampled during a PRECHARGE command to determine whether the PRECHARGE

applies to one bank (A10 LOW) or all banks (A10 HIGH). If only one bank is to be precharged, the bank is

selected by BA0, BA1. The address inputs also provide the op-code during a MODE REGISTER SET com-

mand. BA0 and BA1 define which mode register is loaded during the MODE REGISTER SET command

(MRS or EMRS).

DQ I/O Data Input/Output : Data bus

LDQS,(U)DQS I/O

Data Strobe : Output with read data, input with write data. Edge-aligned with read data, centered in write

data. Used to capture write data. For the x16, LDQS corresponds to the data on

DQ0~D7 ; UDQS corresponds to the data on DQ8~DQ15.

LDQS is NC on x4 and x8.

NC - No Connect : No internal electrical connection is present.

VDDQ Supply DQ Power Supply : +2.5V ± 0.2V.

VSSQ Supply DQ Ground.

VDD Supply Power Supply : +2.5V ± 0.2V.

VSS Supply Ground.

VREF Input SSTL_2 reference voltage.

- 9 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

8. Command Truth Table (V=Valid, X=Don′t Care, H=Logic High, L=Logic Low)

NOTE :

1. OP Code : Operand Code. A0 ~ A12& BA0 ~ BA1 : Program keys. (@EMRS/MRS)

2. EMRS/MRS can be issued only at all banks precharge state.

A new command can be issued 2 clock cycles after EMRS or MRS.

3. Auto refresh functions are same as the CBR refresh of DRAM.

The automatical precharge without row precharge command is meant by "Auto".

Auto/self refresh can be issued only at all banks precharge state.

4. BA0 ~ BA1 : Bank select addresses.

If both BA0 and BA1 are "Low" at read, write, row active and precharge, bank A is selected.

If BA0 is "High" and BA1 is "Low" at read, write, row active and precharge, bank B is selected.

If BA0 is "Low" and BA1 is "High" at read, write, row active and precharge, bank C is selected.

If both BA0 and BA1 are "High" at read, write, row active and precharge, bank D is selected.

5. If A10/AP is "High" at row precharge, BA0 and BA1 are ignored and all banks are selected.

6. During burst write with auto precharge, new read/write command can not be issued.

Another bank read/write command can be issued after the end of burst.

New row active of the associated bank can be issued at tRP after the end of burst.

7. Burst stop command is valid at every burst length.

8. DM(x4/8) sampled at the rising and falling edges of the DQS and Data-in are masked at the both edges (Write DM latency is 0).

UDM/LDM(x16 only) sampled at the rising and falling edges of the UDQS/LDQS and Data-in are masked at the both edges

(Write UDM/LDM latency is 0).

9. This combination is not defined for any function, which means "No Operation(NOP)" in DDR SDRAM.

COMMAND CKEn-1 CKEn CS RAS CAS WE BA0,1 A10/AP A0 ~ A9,

A11 ~ A12 NOTE

Refresh

Auto Refresh HHLL L H X 3

Self

Refresh

Entry L 3

Exit L H LH H H X3

HX X X 3

Bank Active & Row Addr. H X L L H H V Row Address

Read &

Column Address

Auto Precharge Disable HXLHLHV LColumn

Address

Auto Precharge Enable H4

Write &

Column Address

Auto Precharge Disable HXLHLLV LColumn

Address

Auto Precharge Enable H4, 6

Burst Stop H X L H H L X 7

Precharge Bank Selection HXLLHL

VL X

All Banks XH 5

Active Power Down Entry H L HX X X

XLV V V

Exit L H X X X X

Precharge Power Down Mode

Entry H L HX X X

LH H H

Exit L H HX X X

LV V V

DM(UDM/LDM for x16 only) H X X 8

No operation (NOP) : Not defined H X HX X X X9

LH H H 9

- 10 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

1M x 16Bit x 4 Banks Double Data Rate SDRAM

9. General Description

The K4H641638Q is 67,108,864 bits of double data rate synchronous DRAM organized as 4x 1,048,576 words by 16bits, fabricated with SAMSUNG′s

high performance CMOS technology. Synchronous features with Data Strobe allow extremely high performance up to 400Mb/s per pin. I/O transactions

are possible on both edges of DQS. Range of operating frequencies, programmable burst length and programmable latencies allow the device to be use-

ful for a variety of high performance memory system applications.

10. Absolute Maximum Rating

NOTE : Permanent device damage may occur if ABSOLUTE MAXIMUM RATINGS are exceeded.

Functional operation should be restricted to recommend operation condition.

Exposure to higher than recommended voltage for extended periods of time could affect device reliability.

11. DC Operating Conditions Recommended operating conditions(Voltage referenced to VSS=0V, TA=0 to 70°C)

NOTE :

1. VREF is expected to be equal to 0.5*VDDQ of the transmitting device, and to track variations in the dc level of same. Peak-to peak noise on VREF may not exceed +/-2% of the

dc value.

2. VTT is not applied directly to the device. VTT is a system supply for signal termination resistors, is expected to be set equal to VREF, and must track variations in the DC level

of VREF,

3. VID is the magnitude of the difference between the input level on CK and the input level on CK.

4. The ratio of the Pull-up current to the Pull-down current is specified for the same temperature and voltage, over the entire temperature and voltage range, for device drain to

source voltages from 0.25V to 1.0V. For a given output, it represents the maximum difference between Pull-up and Pull-down drivers due to process variation. The full varia-

tion in the ratio of the maximum to minimum Pull-up and Pull-down current will not exceed 1.7 for device drain to source voltages from 0.1 to 1.0.

Parameter Symbol Value Unit

Voltage on any pin relative to VSS VIN, VOUT -0.5 ~ 3.6 V

Voltage on VDD & VDDQ supply relative to VSS VDD, VDDQ 1.0 ~ 3.6 V

Storage temperature TSTG -55 ~ +150 °C

Power dissipation PD1W

Short circuit current IOS 50 mA

Parameter Symbol Min Max Unit NOTE

Supply voltage VDD 2.3 2.7 V

I/O Supply voltage VDDQ 2.3 2.7 V

I/O Reference voltage VREF 0.49*VDDQ 0.51*VDDQ V1

I/O Termination voltage(system) VTT VREF-0.04 VREF+0.04 V2

Input logic high voltage VIH(DC) VREF+0.15 VDDQ+0.3 V

Input logic low voltage VIL(DC) -0.3 VREF-0.15 V

Input Voltage Level, CK and CK inputs VIN(DC) -0.3 VDDQ+0.3 V

Input Differential Voltage, CK and CK inputs VID(DC) 0.36 VDDQ+0.6 V3

V-I Matching: Pull-up to Pull-down Current Ratio VI(Ratio) 0.71 1.4 - 4

Input leakage current II-2 2 uA

Output leakage current IOZ -5 5uA

Output High Current(Full strengh driver) ; VOUT=VDDQ-0.388V IOH -13.8 -16.1 mA

Output Low Current(Full strengh driver) ; VOUT=0.388V IOL 16.5 19.2 mA

Output High Current(Week strengh driver) ; VOUT=VDDQ-0.538V IOH -18.2 -21.8 mA

Output Low Current(Week strengh driver) ; VOUT=0.538V IOL 20.2 24.5 mA

Output High Current(Mached strengh driver) ; VOUT=VDDQ-0.6505V IOH -15.5 -18.9 mA

Output Low Current(Mached strengh driver) ; VOUT=0.6505V IOL 17 21.3 mA

- 11 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

12. DDR SDRAM Spec Items & Test Conditions

13. Input/Output Capacitance (TA= 25°C, f=100MHz)

NOTE :

1.These values are guaranteed by design and are tested on a sample basis only.

2. Although DM is an input -only pin, the input capacitance of this pin must model the input capacitance of the DQ and DQS pins.

This is required to match signal propagation times of DQ, DQS, and DM in the system.

3. Unused pins are tied to ground.

4. This parameter is sampled. VDDQ = +2.5V +0.2V, VDD = +2.5V+0.2V. For all devices, f=100MHz, tA=25°C, VOUT(DC) = VDDQ/2,

VOUT(peak to peak) = 0.2V. DM inputs are grouped with I/O pins - reflecting the fact that they are matched in loading (to facilitate trace matching at the

board level).

Conditions Symbol

Operating current - One bank Active-Precharge;

tRC=tRCmin; tCK=5ns for DDR400;

DQ,DM and DQS inputs changing once per clock cycle;

address and control inputs changing once every two clock cycles.

IDD0

Operating current - One bank operation ; One bank open, BL=4, Reads

- Refer to the following page for detailed test condition IDD1

Precharge power-down standby current; All banks idle; power - down mode;

CKE = <VIL(max); tCK=5ns for DDR400;

VIN = VREF for DQ,DQS and DM.

IDD2P

Precharge Floating standby current; CS > =VIH(min);All banks idle; CKE > = VIH(min); tCK=5ns for DDR400; Address and other

control inputs changing once per clock cycle; VIN = VREF for DQ,DQS and DM IDD2F

Precharge Quiet standby current; CS > = VIH(min); All banks idle;

CKE > = VIH(min); tCK=5ns for DDR400

; Address and other control inputs stable at >= VIH(min) or =<VIL(max); VIN = VREF for DQ ,DQS and DM

IDD2Q

Active power - down standby current ; one bank active; power-down mode;

CKE=< VIL (max); tCK=5ns for DDR400;

VIN = VREF for DQ,DQS and DM

IDD3P

Active standby current; CS >= VIH(min); CKE>=VIH(min);

one bank active; tRC=tRASmax; tCK=5ns for DDR400; DQ, DQS and DM inputs changing twice per clock cycle; address and

other control inputs changing once per clock cycle

IDD3N

Operating current - burst read; Burst length = 2; reads; continuous burst; One bank active; address and control inputs changing

once per clock cycle; CL=2 at tCK=5ns for DDR400; 50% of data changing on every transfer; lout = 0 m A IDD4R

Operating current - burst write; Burst length = 2; writes; continuous burst;

One bank active address and control inputs changing once per clock cycle; tCK=5ns for DDR400; DQ, DM and DQS inputs

changing twice per clock cycle, 50% of input data changing at every burst

IDD4W

Auto refresh current; tRC = tRFC(min) which is 14*tCK for DDR400 at tCK=5ns; distributed refresh IDD5

Self refresh current; CKE =< 0.2V; External clock on; tCK=5ns for DDR400. IDD6

Operating current - Four bank operation ; Four bank interleaving with BL=4

-Refer to the following page for detailed test condition IDD7A

Parameter Symbol Min Max DeltaCap(max) Unit NOTE

Input capacitance

(A0 ~ A12, BA0 ~ BA1, CKE, CS, RAS,CAS, WE)CIN1 14 0.5pF4

Input capacitance( CK, CK ) CIN2 1 5 0.25 pF 4

Data & DQS input/output capacitance COUT 16.5

0.5

pF 1,2,3,4

Input capacitance(DM for x4/8, UDM/LDM for x16) CIN3 1 6.5 pF 1,2,3,4

- 12 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

14. Detailed test condition for DDR SDRAM IDD1 & IDD7A

IDD1 : Operating current: One bank operation

1. Typical Case: VDD = 2.5V, T= 25°C

Worst Case : VDD = 2.7V, T= 10°C

2. Only one bank is accessed with tRC(min), Burst Mode, Address and Control inputs on NOP edge are changing once

per clock cycle. lout = 0mA

3. Timing patterns

- CC(200Mhz,CL = 3) : tCK = 5ns, CL = 3, BL = 4, tRCD = 3*tCK , tRC = 11*tCK, tRAS = 8*tCK

Read : A0 N N R0 N N N N P0 N N - repeat the same timing with random address changing

*50% of data changing at every transfer

Legend : A=Activate, R=Read, W=Write, P=Precharge, N=DESELECT

IDD7A : Operating current: Four bank operation

1. Typical Case: VDD = 2.5V, T=25°C

Worst Case : VDD = 2.7V, T= 10°C

2. Four banks are being interleaved with tRC(min), Burst Mode, Address and Control inputs on NOP edge are not

changing. lout = 0mA

3. Timing patterns

- CC(200Mhz,CL = 3) : tCK = 5ns, CL = 3, BL = 4, tRCD = 3*tCK , tRC = 11*tCK, tRAS = 8*tCK

Read : A0 N A1 R0 A2 R1 A3 R2 N R3 A0 N A1 R0 - repeat the same timing with random address changing

*50% of data changing at every transfer

Legend : A=Activate, R=Read, W=Write, P=Precharge, N=DESELECT

- 13 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

15. DDR SDRAM IDD Spec Table

Symbol 4Mx16 (K4H641638Q)

CC(DDR400@CL=3)

IDD0 50

IDD1 60

IDD2P 3

IDD2F 25

IDD2Q 20

IDD3P 5

IDD3N 30

IDD4R 90

IDD4W 70

IDD5 80

IDD6 Normal 2

IDD7A 90

- 14 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

16. AC Operating Conditions

NOTE :

1. VID is the magnitude of the difference between the input level on CK and the input level on CK.

2. The value of VIX is expected to equal 0.5*VDDQ of the transmitting device and must track variations in the dc level of the same.

3. VREF is expected to equal VDDQ/2 of the transmitting device and to track variations in the DC level of the same.

Peak-to-peak noise (non-common mode) on VREF may not exceed ±2 percent of the DC value. Thus, from VDDQ/2, VREF is allowed ±25mV for DC error and an additional

±25mV for AC noise. This measurement is to be taken at the nearest VREF by-pass capacitor.

17. AC Overshoot/Undershoot specification for Address and Control Pins

Parameter/Condition Symbol Min Max Unit NOTE

Input High (Logic 1) Voltage, DQ, DQS and DM signals VIH(AC) VREF + 0.31 V

Input Low (Logic 0) Voltage, DQ, DQS and DM signals. VIL(AC) VREF - 0.31 V

Input Differential Voltage, CK and CK inputs VID(AC) 0.7 VDDQ+0.6 V1

Input Crossing Point Voltage, CK and CK inputs VIX(AC) 0.5*VDDQ-0.2 0.5*VDDQ+0.2 V2

I/O Reference Voltage VREF(AC) 0.45 x VDDQ 0.55 x VDDQ V 3

Parameter Specification

DDR400 DDR333

Maximum peak amplitude allowed for overshoot 1.5 V 1.5 V

Maximum peak amplitude allowed for undershoot 1.5 V 1.5 V

The area between the overshoot signal and VDD must be less than or equal to 4.5 V-ns 4.5 V-ns

The area between the undershoot signal and GND must be less than or equal to 4.5 V-ns 4.5 V-ns

-1

-2

-3

-4

-5

0.5

0.6875

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.3125

6.5

7.0

VDD Overshoot

Maximum Amplitude = 1.5V

Area

Maximum Amplitude = 1.5V

undershoot

GND

Volts (V)

Tims(ns)

AC overshoot/Undershoot Definition

- 15 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

18. Overshoot/Undershoot specification for Data, Strobe and Mask Pins

Parameter Specification

DDR400

Maximum peak amplitude allowed for overshoot 1.2 V

Maximum peak amplitude allowed for undershoot 1.2 V

The area between the overshoot signal and VDD must be less than or equal to 2.4 V-ns

The area between the undershoot signal and GND must be less than or equal to 2.4 V-ns

-1

-2

-3

-4

-5

0 0.5 1.0 1.42 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 5.68 6.0 6.5 7.0

VDDQ

Overshoot

Maximum Amplitude = 1.2V

Area

Maximum Amplitude = 1.2V

undershoot

GND

Volts (V)

Tims(ns)

DQ/DM/DQS AC overshoot/Undershoot Definition

- 16 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

19. AC Timing Parameters & Specifications

Parameter Symbol

(DDR400@CL=3.0) Unit NOTE

Min Max

Row cycle time tRC 55 ns

Refresh row cycle time tRFC 70 ns

Row active time tRAS 40 70K ns

RAS to CAS delay tRCD 15 ns

Row precharge time tRP 15 ns

Row active to Row active delay tRRD 10 ns

Write recovery time tWR 15 ns

Last data in to Read command tWTR 2 tCK

Clock cycle time

CL=2.0

tCK

--ns

CL=2.5 6 12 ns

CL=3.0 5 10

Clock high level width tCH 0.45 0.55 tCK

Clock low level width tCL 0.45 0.55 tCK

DQS-out access time from CK/CK tDQSCK -0.55 +0.55 ns

Output data access time from CK/CK tAC -0.65 +0.65 ns

Data strobe edge to output data edge TSOP tDQSQ -0.4ns22

FBGA - 0.4 ns 22

Read Preamble tRPRE 0.9 1.1 tCK

Read Postamble tRPST 0.4 0.6 tCK

CK to valid DQS-in tDQSS 0.72 1.28 tCK

DQS-in setup time tWPRES 0 ns 13

DQS-in hold time tWPRE 0.25 tCK

DQS falling edge to CK rising-setup time tDSS 0.2 tCK

DQS falling edge from CK rising-hold time tDSH 0.2 tCK

DQS-in high level width tDQSH 0.35 tCK

DQS-in low level width tDQSL 0.35 tCK

Address and Control Input setup time(fast) tIS 0.6 ns 15, 17~19

Address and Control Input hold time(fast) tIH 0.6 ns 15, 17~19

Address and Control Input setup time(slow) tIS 0.7 ns 16~19

Address and Control Input hold time(slow) tIH 0.7 ns 16~19

Data-out high impedance time from CK/CK tHZ -0.65 +0.65 ns 11

Data-out low impedance time from CK/CK tLZ -0.65 +0.65 ns 11

Mode register set cycle time tMRD 10 ns

DQ & DM setup time to DQS tDS 0.4 ns j, k

DQ & DM hold time to DQS tDH 0.4 ns j, k

Control & Address input pulse width tIPW 2.2 ns 18

DQ & DM input pulse width tDIPW 1.75 ns 18

Exit self refresh to non-Read command tXSNR 75 ns

Exit self refresh to read command tXSRD 200 tCK

Refresh interval time tREFI 15.6 us 14

Output DQS valid window tQH tHP

-tQHS -ns 21

Clock half period tHP tCLmin

or tCHmin -ns 20, 21

Data hold skew factor TSOP tQHS 0.5 ns 21

FBGA tQHS 0.5 ns 21

DQS write postamble time tWPST 0.4 0.6 tCK 12

Active to Read with Auto precharge

command tRAP 15

Autoprecharge write recovery +

Precharge time tDAL

(tWR/tCK)

(tRP/tCK)

tCK 23

Power Down Exit tPDEX 1tCK

- 17 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

20. System Characteristics for DDR SDRAM

The following specification parameters are required in systems using DDR400 and DDR333 devices to ensure proper system performance. these char-

acteristics are for system simulation purposes and are guaranteed by design.

[ Table 1 ] Input Slew Rate for DQ, DQS, and DM

[ Table 2 ] Input Setup & Hold Time Derating for Slew Rate

[ Table 3 ] Input/Output Setup & Hold Time Derating for Slew Rate

[ Table 4 ] Input/Output Setup & Hold Derating for Rise/Fall Delta Slew Rate

[ Table 5 ] Output Slew Rate Characteristice (x4, x8 Devices only)

[ Table 6 ] Output Slew Rate Characteristice (x16 Devices only)

[ Table 7 ] Output Slew Rate Matching Ratio Characteristics

AC CHARACTERISTICS DDR400 DDR333 Units NOTE

PARAMETER SYMBOL MIN MAX MIN MAX

DQ/DM/DQS input slew rate measured between

VIH(DC), VIL(DC) and VIL(DC), VIH(DC) DCSLEW 0.5 4.0 0.5 4.0 V/ns a, l

Input Slew Rate ∆tIS ∆tIH Units NOTE

0.5 V/ns 0 0 ps i

0.4 V/ns +50 0 ps i

0.3 V/ns +100 0 ps i

Input Slew Rate ∆tDS ∆tDH Units NOTE

0.5 V/ns 0 0 ps k

0.4 V/ns +75 +75 ps k

0.3 V/ns +150 +150 ps k

Delta Slew Rate ∆tDS ∆tDH Units NOTE

+/- 0.0 V/ns 0 0 ps j

+/- 0.25 V/ns +50 +50 ps j

+/- 0.5 V/ns +100 +100 ps j

Slew Rate Characteristic Typical Range

(V/ns)

Minimum

(V/ns)

Maximum

(V/ns) NOTE

Pull-up Slew Rate 1.2 ~ 2.5 1.0 4.5 a,c,d,f,g,h

Pull-down slew 1.2 ~ 2.5 1.0 4.5 b,c,d,f,g,h

Slew Rate Characteristic Typical Range

(V/ns)

Minimum

(V/ns)

Maximum

(V/ns) NOTE

Pull-up Slew Rate 1.2 ~ 2.5 0.7 5.0 a,c,d,f,g,h

Pull-down slew 1.2 ~ 2.5 0.7 5.0 b,c,d,f,g,h

AC CHARACTERISTICS DDR400 DDR333 NOTE

PARAMETER MIN MAX MIN MAX

Output Slew Rate Matching Ratio (Pull-up to Pull-down) 0.67 1.5 0.67 1.5 e, l

Figure 1. Timing Reference Load

- 18 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

21. Component Notes

1. All voltages referenced to VSS.

2. Tests for ac timing, IDD, and electrical, ac and dc characteristics, may be conducted at nominal reference/supply voltage levels,

but the related specifications and device operation are guaranteed for the full voltage range specified.

3. Figure 1 represents the timing reference load used in defining the relevant timing parameters of the part. It is not intended to be

either a precise representation of the typical system environment nor a depiction of the actual load presented by a production

tester. System designers will use IBIS or other simulation tools to correlate the timing reference load to a system environment.

Manufacturers will correlate to their production test conditions (generally a coaxial transmission line terminated at the tester electronics).

4. AC timing and IDD tests may use a VIL to VIH swing of up to 1.5 V in the test environment, but input timing is still referenced to

VREF (or to the crossing point for CK/CK), and parameter specifications are guaranteed for the specified ac input levels under normal

use conditions. The minimum slew rate for the input signals is 1 V/ns in the range between VIL(AC) and VIH(AC).

5. The ac and dc input level specifications are as defined in the SSTL_2 Standard (i.e., the receiver will effectively switch as a result

of the signal crossing the ac input level and will remain in that state as long as the signal does not ring back above (below) the dc

input LOW (HIGH) level.

6. Inputs are not recognized as valid until VREF stabilizes. Exception: during the period before VREF stabilizes, CKE ≤ 0.2VDDQ is

recognized as LOW.

7. Enables on.chip refresh and address counters.

8. IDD specifications are tested after the device is properly initialized.

9. The CK/CK input reference level (for timing referenced to CK/CK) is the point at which CK and CK cross; the input reference level

for signals other than CK/CK, is VREF

10. The output timing reference voltage level is VTT

11. tHZ and tLZ transitions occur in the same access time windows as valid data transitions. These parameters are not referenced to

a specific voltage level but specify when the device output is no longer driving (HZ), or begins driving (LZ).

12. The maximum limit for this parameter is not a device limit. The device will operate with a greater value for this parameter, but sys

tem performance (bus turnaround) will degrade accordingly.

13. The specific requirement is that DQS be valid (HIGH, LOW, or at some point on a valid transition) on or before this CK edge. A

valid transition is defined as monotonic and meeting the input slew rate specifications of the device. when no writes were previ

ously in progress on the bus, DQS will be transitioning from High- Z to logic LOW. If a previous write was in progress, DQS could

be HIGH, LOW, or transitioning from HIGH to LOW at this time, depending on tDQSS.

14. A maximum of eight AUTO REFRESH commands can be posted to any given DDR SDRAM device.

15. For command/address input slew rate ≥ 1.0 V/ns

16. For command/address input slew rate ≥ 0.5 V/ns and < 1.0 V/ns

17. For CK & CK slew rate ≥ 1.0 V/ns

18. These parameters guarantee device timing, but they are not necessarily tested on each device. They may be guaranteed by

device design or tester correlation.

19. Slew Rate is measured between VOH(AC) and VOL(AC).

Output

VTT

50Ω

30pF

(Vout)

- 19 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

20. Min (tCL, tCH) refers to the smaller of the actual clock low time and the actual clock high time as provided to the device (i.e. this

value can be greater than the minimum specification limits for tCL and tCH).....For example, tCL and tCH are = 50% of the

period, less the half period jitter (tJIT(HP)) of the clock source, and less the half period jitter due to crosstalk (tJIT(crosstalk)) into

the clock traces.

21. tQH = tHP - tQHS, where:

tHP = minimum half clock period for any given cycle and is defined by clock high or clock low (tCH, tCL). tQHS accounts for 1) The

pulse duration distortion of on-chip clock circuits; and 2) The worst case push-out of DQS on one tansition followed by the worst

case pull-in of DQ on the next transition, both of which are, separately, due to data pin skew and output pattern effects, and p-

channel to n-channel variation of the output drivers.

22. tDQSQ

Consists of data pin skew and output pattern effects, and p-channel to n-channel variation of the output drivers for any given cycle.

23. tDAL = (tWR/tCK) + (tRP/tCK)

For each of the terms above, if not already an integer, round to the next highest integer. Example: For DDR400 at CL=3 and

tCK=5ns tDAL = (15 ns / 5 ns) + (15 ns/ 5ns) = (3) + (3)

tDAL = 6 clocks

Figure 3. Pull-down slew rate test load

Figure 2. Pull-up slew rate test load

- 20 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

22. System Notes

a. Pull-up slew rate is characteristized under the test conditions as shown in Figure 2

b. Pull-down slew rate is measured under the test conditions shown in Figure 3

c. Pull-up slew rate is measured between (VDDQ/2 - 320 mV +/- 250 mV)

Pull-down slew rate is measured between (VDDQ/2 + 320 mV +/- 250 mV)

Pull-up and Pull-down slew rate conditions are to be met for any pattern of data, including all outputs switching and only one output

switching.

Example : For typical slew rate, DQ0 is switching

For minmum slew rate, all DQ bits are switching from either high to low, or low to high.

The remaining DQ bits remain the same as for previous state.

d. Evaluation conditions

Typical : 25 °C (T Ambient), VDDQ = 2.5V, typical process

Minimum : 70 °C (T Ambient), VDDQ = 2.3V, slow - slow process

Maximum : 0 °C (T Ambient), VDDQ = 2.7V, fast - fast process

e. The ratio of Pull-up slew rate to Pull-down slew rate is specified for the same temperature and voltage, over the entire temperature

and voltage range. For a given output, it represents the maximum difference between Pull-up and Pull-down drivers due to process

variation.

f. Verified under typical conditions for qualification purposes.

g. TSOPII package divices only.

h. Only intended for operation up to 400 Mbps per pin.

i. A derating factor will be used to increase tIS and tIH in the case where the input slew rate is below 0.5V/ns

as shown in Table 2. The Input slew rate is based on the lesser of the slew rates detemined by either VIH(AC) to VIL(AC) or

VIH(DC) to VIL(DC), similarly for rising transitions.

j. A derating factor will be used to increase tDS and tDH in the case where DQ, DM, and DQS slew rates differ, as shown in Tables 3 & 4.

Input slew rate is based on the larger of AC-AC delta rise, fall rate and DC-DC delta rise, Input slew rate is based on the lesser of the

slew rates determined by either VIH(AC) to VIL(AC) or VIH(DC) to VIL(DC), similarly for rising transitions.

The delta rise/fall rate is calculated as:

{1/(Slew Rate1)} - {1/(Slew Rate2)}

For example : If Slew Rate 1 is 0.5 V/ns and slew Rate 2 is 0.4 V/ns, then the delta rise, fall rate is - 0.5ns/V . Using the table given, this

would result in the need for an increase in tDS and tDH of 100 ps.

k. Table 3 is used to increase tDS and tDH in the case where the I/O slew rate is below 0.5 V/ns. The I/O slew rate is based on the lesser

on the lesser of the AC - AC slew rate and the DC- DC slew rate. The inut slew rate is based on the lesser of the slew rates deter

mined by either VIH(AC) to VIL(AC) or VIH(DC) to VIL(DC), and similarly for rising transitions.

l. DQS, DM, and DQ input slew rate is specified to prevent double clocking of data and preserve setup and hold times. Signal transi

tions through the DC region must be monotonic.

Output

Test point

VSSQ

50Ω

Output

Test point

VDDQ

50Ω

- 21 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

23. Output Drive Strength and Extended Mode Register Set for 64Mb DDR

The 100%, 60%, and 30% or matched impedance drive strength options are required and are defined in External Mode Register (EMRS). The Extended

Mode Register Set stores the data for enabling or disabling DLL and selecting output driver strength. The default value of the extended mode register is

not defined, therefore must be written after power up0 for proper operation. The extended mode register is written by asserting low on CS, RAS, CAS, and

WE. The state of A0, A2 ~ A5, A7 ~ A11and BA1 is written in the mode register in the same cycle as CS, RAS, CAS, and WE going low. The DDR SDRAM

should be in all bank precharge with CKE already high prior to writing into the extended mode register. A1 and A6 are used for setting driver strength to

100%, 60%, or 30%. Two clock cycles are required to complete the write operation in the extended mode register. The mode register contents can be

changed using the same command and clock cycle requirements during operation as long as all banks are in the idle state. A0 is used for DLL enable or

disable. "High" on BA0 is used for EMRS. Refer to the table for specific codes.

BA1 BA0 A11 A10 A9 A8 A7 A6 A5 A4 A3 A2 A1 A0

0 1 RFU must be set to "0" DS1 RFU must be set to "0" DS0 DLL

BA1 Mode

0MRS

1EMRS

A6 A1 Drive Strength Strength Comment

0 0 Full 100%

0 1 weak 60%

1 0 RFU RFU Do not use

11 Matched

impedance 30% Output driver

matches impedance

A0 DLL

0 Enable

1 Disable

Figure 4. I/V characteristics for input/output buffers : Pull-down(above) and Pull-up(below)

- 22 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

24. IBIS : I/V Characteristics for Input and Output Buffers

DDR SDRAM Output Driver V-I Characteristics

DDR SDRAM Output driver characteristics are defined for full and half strength operation as selected by the EMRS bit A1.

Figures 4, 5 and 6 show the driver characteristics graphically, and tables 8, 9 and 10 show the same data in tabular format suitable for

input into simulation tools. The driver characteristcs evaluation conditions are:

Output Driver Characteristic Curves Notes:

1. The full variation in driver current from minimum to maximum process, temperature and voltage will lie within the outer bounding lines the of the V-I

curve of Figures 4, 5 and 6.

2. It is recommended that the "typical" IBIS V-I curve lie within the inner bounding lines of the V-I curves of Figures 4, 5 and 6.

3. The full variation in the ratio of the "typical" IBIS Pull-up to "typical" IBIS Pull-down current should be unity +/- 10%, for device drain to source voltages

from 0.1 to1.0. This specification is a design objective only. It is not guaranteed.

Typical 25×C VDD/VDDQ = 2.5V, typical process

Minimum 70×C VDD/VDDQ = 2.3V, slow-slow process

Maximum 0×C VDD/VDDQ = 2.7V, fast-fast process

Minimum

Typical Low

Typical High

Maximum

100

120

140

160

0.0 0.5 1.0 1.5 2.0 2.5

Iout(mA)

Vout(V)

Pull-down Characteristics for Full Strength Output Driver

Maximum

Typical High

Minumum

Vout(V)

Iout(mA)

-220

-200

-180

-160

-140

-120

-100

-80

-60

-40

-20

0.0 1.0 2.0

Typical Low

Pull-up Characteristics for Full Strength Output Driver

- 23 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

[ Table 8 ] Full Strength Driver Characteristics

Pull-down Current (mA) Pull-up Current (mA)

Voltage

(V)

Typical

Low

Typical

High Minimum Maximum

Typical

Low

Typical

High Minimum Maximum

0.1 6.0 6.8 4.6 9.6 -6.1 -7.6 -4.6 -10.0

0.2 12.2 13.5 9.2 18.2 -12.2 -14.5 -9.2 -20.0

0.3 18.1 20.1 13.8 26.0 -18.1 -21.2 -13.8 -29.8

0.4 24.1 26.6 18.4 33.9 -24.0 -27.7 -18.4 -38.8

0.5 29.8 33.0 23.0 41.8 -29.8 -34.1 -23.0 -46.8

0.6 34.6 39.1 27.7 49.4 -34.3 -40.5 -27.7 -54.4

0.7 39.4 44.2 32.2 56.8 -38.1 -46.9 -32.2 -61.8

0.8 43.7 49.8 36.8 63.2 -41.1 -53.1 -36.0 -69.5

0.9 47.5 55.2 39.6 69.9 -41.8 -59.4 -38.2 -77.3

1.0 51.3 60.3 42.6 76.3 -46.0 -65.5 -38.7 -85.2

1.1 54.1 65.2 44.8 82.5 -47.8 -71.6 -39.0 -93.0

1.2 56.2 69.9 46.2 88.3 -49.2 -77.6 -39.2 -100.6

1.3 57.9 74.2 47.1 93.8 -50.0 -83.6 -39.4 -108.1

1.4 59.3 78.4 47.4 99.1 -50.5 -89.7 -39.6 -115.5

1.5 60.1 82.3 47.7 103.8 -50.7 -95.5 -39.9 -123.0

1.6 60.5 85.9 48.0 108.4 -51.0 -101.3 -40.1 -130.4

1.7 61.0 89.1 48.4 112.1 -51.1 -107.1 -40.2 -136.7

1.8 61.5 92.2 48.9 115.9 -51.3 -112.4 -40.3 -144.2

1.9 62.0 95.3 49.1 119.6 -51.5 -118.7 -40.4 -150.5

2.0 62.5 97.2 49.4 123.3 -51.6 -124.0 -40.5 -156.9

2.1 62.9 99.1 49.6 126.5 -51.8 -129.3 -40.6 -163.2

2.2 63.3 100.9 49.8 129.5 -52.0 -134.6 -40.7 -169.6

2.3 63.8 101.9 49.9 132.4 -52.2 -139.9 -40.8 -176.0

2.4 64.1 102.8 50.0 135.0 -52.3 -145.2 -40.9 -181.3

2.5 64.6 103.8 50.2 137.3 -52.5 -150.5 -41.0 -187.6

2.6 64.8 104.6 50.4 139.2 -52.7 -155.3 -41.1 -192.9

2.7 65.0 105.4 50.5 140.8 -52.8 -160.1 -41.2 -198.2

Figure 5. I/V characteristics for input/output buffers : Pull-down(above) and Pull-up(below)

- 24 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

Iout(mA)

Minimum

Typical Low

Typical High

Maximum

0.0 1.0 2.0

Iout(mA)

Vout(V)

Pull-down Characteristics for Weak Output Driver

Maximum

Typical High

Minumum

Vout(V)

Iout(mA)

-90

-80

-70

-60

-50

-40

-30

-20

-10

0.0 1.0 2.0

Typical Low

Pull-up Characteristics for Weak Output Driver

- 25 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

[ Table 9 ] Weak Driver Characteristics

Pull-down Current (mA) Pull-up Current (mA)

Voltage

(V)

Typical

Low

Typical

High Minimum Maximum

Typical

Low

Typical

High Minimum Maximum

0.1 3.4 3.8 2.6 5.0 -3.5 -4.3 -2.6 -5.0

0.2 6.9 7.6 5.2 9.9 -6.9 -8.2 -5.2 -9.9

0.3 10.3 11.4 7.8 14.6 -10.3 -12.0 -7.8 -14.6

0.4 13.6 15.1 10.4 19.2 -13.6 -15.7 -10.4 -19.2

0.5 16.9 18.7 13.0 23.6 -16.9 -19.3 -13.0 -23.6

0.6 19.6 22.1 15.7 28.0 -19.4 -22.9 -15.7 -28.0

0.7 22.3 25.0 18.2 32.2 -21.5 -26.5 -18.2 -32.2

0.8 24.7 28.2 20.8 35.8 -23.3 -30.1 -20.4 -35.8

0.9 26.9 31.3 22.4 39.5 -24.8 -33.6 -21.6 -39.5

1.0 29.0 34.1 24.1 43.2 -26.0 -37.1 -21.9 -43.2

1.1 30.6 36.9 25.4 46.7 -27.1 -40.3 -22.1 -46.7

1.2 31.8 39.5 26.2 50.0 -27.8 -43.1 -22.2 -50.0

1.3 32.8 42.0 26.6 53.1 -28.3 -45.8 -22.3 -53.1

1.4 33.5 44.4 26.8 56.1 -28.6 -48.4 -22.4 -56.1

1.5 34.0 46.6 27.0 58.7 -28.7 -50.7 -22.6 -58.7

1.6 34.3 48.6 27.2 61.4 -28.9 -52.9 -22.7 -61.4

1.7 34.5 50.5 27.4 63.5 -28.9 -55.0 -22.7 -63.5

1.8 34.8 52.2 27.7 65.6 -29.0 -56.8 -22.8 -65.6

1.9 35.1 53.9 27.8 67.7 -29.2 -58.7 -22.9 -67.7

2.0 35.4 55.0 28.0 69.8 -29.2 -60.0 -22.9 -69.8

2.1 35.6 56.1 28.1 71.6 -29.3 -61.2 -23.0 -71.6

2.2 35.8 57.1 28.2 73.3 -29.5 -62.4 -23.0 -73.3

2.3 36.1 57.7 28.3 74.9 -29.5 -63.1 -23.1 -74.9

2.4 36.3 58.2 28.3 76.4 -29.6 -63.8 -23.2 -76.4

2.5 36.5 58.7 28.4 77.7 -29.7 -64.4 -23.2 -77.7

2.6 36.7 59.2 28.5 78.8 -29.8 -65.1 -23.3 -78.8

2.7 36.8 59.6 28.6 79.7 -29.9 -65.8 -23.3 -79.7

Figure 6. I/V characteristics for input/output buffers:Pull-down(above) and Pull-up(below)

- 26 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

Pull-down Characteristics for Matched Output Driver

0.0 1.0 2.0

Minimum

Maximum

Iout(mA)

Vout(V)

Pull-up Characteristics for Matched Output Driver

Maximum

Minumum

Vout(V)

Iout(mA)

-70

-60

-50

-40

-30

-20

-10

0.0 1.0 2.0

- 27 -

K4H641638Q datasheet DDR SDRAM

Rev. 1.1

[ Table 10 ] Matched Driver Characteristics

Pull-down Current(mA) pull-up Current (mA)

Voltage

(V) Minimum Maximum Minimum Maximum

0 0.0 0.0 0.0 0.0

0.2 3.6 7.8 -4.4 -8.8

0.4 7.3 15.8 -8.8 -15.7

0.6 11.0 23.1 -13.3 -23.0

0.8 14.6 29.4 -17.3 -29.4

1.0 16.8 35.5 -18.6 -35.4

1.2 18.3 41.0 -18.9 -41.0

1.4 18.8 46.1 -19.0 -46.0

1.6 19.0 50.5 -19.3 -50.3

1.8 19.6 53.8 -19.5 -53.8

2.0 19.7 57.3 -19.6 -57.2

2.2 19.8 60.1 -19.7 -60.1