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Measuring Capacitance
This page
shows how to measure input capacitance on an inverter, first using AC Analysis frequency
response and then again using transient analysis for comparison.
1) Procedure
to Measure Capacitance using AC Analysis
This example shows how to measure input capacitance on an inverter input using
AC analysis. Below is the HSPICE source (omitting the transistor
model setup). See the comments which explain how capacitance "c_comp"
is measured. All lines beginning with asterisk (*) are comments in HSPICE.
Any text after a "$" is also a comment. The HSPICE output file with the
measured capacitance is also
shown after the source code.
A) HSPICE
SOURCE CODE USING AC ANALYSIS
********===============================================================********
***************** Power Supplies Parameters and Connection ****************
********===============================================================********
*
* Set frequency parameter to 100MHz and pi constant:
*
.param pfreq = 100x
$ Input Frequency in AC analysis, 100MHz
+
pi = 3.1415926535 $ value of pi
*
* Global Supply parameters:
*
.param pvss = 0.00V
+ pvdd = 1.50V
+ pvdd2 = 'pvdd * 0.50'
+ pvih = 'pvss'
+ pvil = 'pvdd'
*
* Supply Setup -
VVDD VDD 0 DC 'pvdd'
VVSS VSS 0 DC 'pvss'
********===============================================================********
*
*
********===============================================================********
***************** Circuit Hookup and Output Loading ****************
********===============================================================********
*
XINV VDD VSS A Z
INV WP=2.04u WN=1.42u
*
.NODESET V(A)='pvdd2' $ Initial DC Bias for AC
Sweep
********===============================================================********
*
********===============================================================********
***************** AC ANALYSIS and C_Comp Measurement
*****************
********===============================================================********
*
* This performs a frequency sweep by 10 points per decade from 1kHz to 1GHz:
*
.AC DEC 10 1K 1000x
*
* #####################################################################
* ################ Start AC Analysis for net: "A"
##############
* ################ >> Can only run one net at a time <<
##############
* #####################################################################
*
* Net "A" voltage source has vdd/2 DC bias and 1mV RMS AC bias:
*
VINAC_A A VSS DC 'pvdd2' AC 1mV
*
* .NET starts the AC Network Analysis (VINAC.. is input voltage source) :
* -------------------------------------------------------------------
* Syntax for 1-port : .net VINAC <--- using this one and measuring ZIN.
* Syntax for 2-ports: .net v(out_node) VINAC
* ------------------------------------------
*
.NET VINAC_A
*
* These are the real (ZR_A) and imaginary parts (ZI_A) of input impedance (ZIN)
:
*
*measure ac ZR_A FIND ZIN(R) AT = 'pfreq' (commented out/see below for "res_A")
.measure ac ZI_A FIND ZIN(I) AT = 'pfreq'
*
* General Impedance: ZIN = ZR + j x ZI (where j = sqrt(-1)
*
* so we have: j x ZI = 1/(j x omega x Cin) --> ZI = -1/(omega x Cin)
*
* ---> Cin = abs (1/(omega x ZI_A)), where omega = 2 x pi x f
and abs is absolute value.
* ---> Cin = abs (1/(2 x pi x f x ZI_A))
*
.measure ac c_comp_A param ='abs(1.0/(2.0*pi*pfreq*ZI_A))'
.measure ac res_A FIND ZIN(R) AT = 'pfreq'
*
*
********===============================================================********
**************** Output Signals
****************
********===============================================================********
*
.probe ac ZIN(R) ZIN(I)
*
********===============================================================********
B) HSPICE
OUTPUT FOR AC ANALYSIS (".lis" file) (run on linux box)
Here is a portion of the HSPICE output
".lis"
file. Marked in blue we see first the Nodal
Capacitance Table
estimates our
capacitance to be 4.526fF,
and the result of the AC analysis is 6.845fF using our setup.
****** HSPICE -- W-2004.09 (20040730) 11:53:10 05/19/2007 linux
******
r0: test_cap_tran, c_comp typ. 25c
****** operating point information tnom= 27.000 temp= 65.000
******
***** operating point status is all simulation time is 0.
nodal capacitance table
node = cap node = cap node = cap
+0:a = 4.526f 0:vdd =
8.432f 0:vss = 6.441f
+0:z = 4.720f
r0: test_cap_tran, c_comp typ. 25c
****** ac analysis tnom= 27.000 temp= 65.000
******
zi_a=-232.498k
c_comp_a= 6.845f
res_a= 471.341
***** job concluded
****** HSPICE -- W-2004.09 (20040730) 11:53:10 05/19/2007
******
r0: test_cap_tran, c_comp typ. 25c
****** job statistics summary tnom= 27.000 temp= 65.000
******
total memory used 473 kbytes
# nodes = 5 # elements= 5
# diodes= 0 # bjts = 0 # jfets = 0 # mosfets = 2
analysis time # points tot. iter conv.iter
op point 0.00 1 7
ac analysis 0.00 61 61
readin 0.11
errchk 0.03
setup 0.01
output 0.00
total cpu time 0.15 seconds
job started at 11:53:10 05/19/2007
job ended at 11:53:13 05/19/2007
2) Alternate Method
to Measure Capacitance using Transient Analysis
This example shows how to measure input capacitance on an inverter input using
transient analysis. Below is the HSPICE source, omitting the
transistor model setup. See the comments which explain how
capacitance "c_comp" is measured. All lines beginning with asterisk are
comments in HSPICE. Any text after a "$" is also a comment. The
HSPICE output with result is also shown after the source code.
This is done using the formula for current through a capacitor: I =
C x delta-V/delta-T, or
C = I x
delta-T/delta-V
The final
result will be the average of the above formula run twice: First with a
rising input, and then with a falling input. Answer is shown in
blue
below.
A) HSPICE
SOURCE CODE USING TRANSIENT ANALYSIS
* Set triangle pulse timing parameters here :
* -----------------------------------------
.param ptr = 1.0n $ Input Pulse rise time
= 1ns
+ ptf = 1.0n $ Input Pulse fall time
= 1ns
+ ptd = 1.0n $ delay to start
pulse
+ pstop = 'ptd+ptr+ptf' $ End of simulation
* Global Supply parameters:
.
.param pvss = 0.00V
+ pvdd = 1.50V
+ pvdd2 = 'pvdd * 0.50'
+ pvih = 'pvdd2 + 250mV' $ gives delta-V = 0.5V
+ pvil = 'pvdd2 - 250mV'
*
* Supply Setup
* -----------------------------
VVDD VDD 0 DC 'pvdd'
VVSS VSS 0 DC 'pvss'
*
********===============================================================********
***************** Circuit Hookup
****************
********===============================================================********
*
XINV VDD VSS A Z
INV WP=2.04u WN=1.42u
********===============================================================********
***************** TRANSIENT ANALYSIS
*****************
********===============================================================********
*
*----------------
.TRAN 10p 'pstop'
*----------------
*
* Note: Pulse below starts at Vdd/2 just to get cap. table value at A = Vdd/2.
* Then you have triangle pulse with same slope at each side:
*
VA A VSS PWL (0.00n 'pvdd2' 'ptd/5' 'pvil' 'ptd' 'pvil' 'ptd+ptr' 'pvih' 'ptd+ptr+ptf'
'pvil')
*
* Note: Slew rate = (pvih -
pvil) / (ptr) = 0.5V/1.0 nS
*
********===============================================================********
***************** Measure Statements
****************
********===============================================================********
*
* This assumes node "A" is your net for cap measurement, and "VA"
* is the PWL source with slow (0.5V/nS) ramp.
*
* CALCULATE THE 20/80/50% LEVELS:
.measure tran ptrp20m param = 'pvil + (pvih-pvil)*0.20'
.measure tran ptrp80m param = 'pvil + (pvih-pvil)*0.80'
.measure tran ptrp50m param = 'pvil + (pvih-pvil)*0.50'
*
.measure tran DELTA_V param = '(pvih-pvil)*0.60'
$ Using 20-80% of swing for DELTA_V, which is 60%
*
* Here_are_IIH_and_IIL for Rising Waveform:
.measure tran IIHR FIND I(VA) WHEN V(A) = ptrp80m td='ptd/2'
.measure tran IILR FIND I(VA) WHEN V(A) = ptrp20m td='ptd/2'
*
* Here_are_IIH_and_IIL for Falling Waveform:
.measure tran IIHF FIND I(VA) WHEN V(A) = ptrp80m td='ptd+ptr'
.measure tran IILF FIND I(VA) WHEN V(A) = ptrp20m td='ptd+ptr'
*
* Here is the 20-80% Rise Time:
.measure tran DT_R trig V(A) val='ptrp20m' td='ptd/2' rise=1
+
targ V(A) val='ptrp80m' td='ptd/2' rise=1
*
* Here is the 80-20% Fall Time:
.measure tran DT_F trig V(A) val='ptrp80m' td='ptd/2' fall=1
+
targ V(A) val='ptrp20m' td='ptd/2' fall=1
*
* Now use C = I x
delta-T/delta-V:
.measure tran C_compR param = 'abs(IIHR-IILR) * DT_R / (DELTA_V)'
$ Capacitance for Rising Pulse
.measure tran C_compF param = 'abs(IIHF-IILF) * DT_F / (DELTA_V)'
$ Capacitance for Falling Pulse
.measure tran C_comp_avg param = '(C_compR+C_compF) / 2.0'
$ Average value
*
*
********===============================================================********
**************** Output Signals
****************
********===============================================================********
*
* Power Supplies and Global Signals :
*
.probe tran V(VDD) V(VSS) V(A) V(Z)
*
********===============================================================********
B) HSPICE OUTPUT (".lis" FILE)
Here is a portion of the output .lis file. The result is
slightly less than the AC method using the transient method which averages the
currents for the rising and falling inputs.
******
r0: test_cap_tran, c_comp typ. 25c
****** transient analysis tnom= 27.000 temp= 65.000
******
ptrp20m= 600.000m
ptrp80m= 900.000m
ptrp50m= 750.000m
delta_v= 300.000m
*
iilr= -4.538u
iihr= -2.719u
iihf= 2.688u
iilf= 6.436u
dt_r= 600.000p targ= 1.800n trig= 1.200n
dt_f= 600.000p targ= 2.800n trig= 2.200n
*
c_compr= 3.638f
c_compf= 7.496f
c_comp_avg= 5.567f (Compare to c_comp_a=
6.845f we had before using AC analysis)
***** job concluded
****** HSPICE -- W-2004.09 (20040730) 14:28:16 05/19/2007
******
r0: test_cap_tran, c_comp typ. 25c
****** job statistics summary tnom= 27.000 temp= 65.000
******
total memory used 604 kbytes
# nodes = 5 # elements= 5
# diodes= 0 # bjts = 0 # jfets = 0 # mosfets = 2
analysis time # points tot. iter conv.iter
op point 0.00 1 7
transient 0.01 301 318 156 rev= 0
readin 0.11
errchk 0.04
setup 0.00
output 0.00
total cpu time 0.16 seconds
job started at 14:28:16 05/19/2007
job ended at 14:28:23 05/19/2007
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