1
Exc. 1: Hartley mixer
RF
LO
90
+
IF
Hartley mixer cancells the image sideband: only signal
will appear in IF port, while image is cancelled. This
can be seen using Matlab file hartley.m that convolves
the line spectrums given
90
Do:
• select lower sideband
• select upper sideband
• check the effect of 10% error in LO phase shift
LO
signal
image
RF
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
2
Exc. 2: AM/AM test
In amam.i AM/AM and AM/PM curves are simulated
using 1-tone harmonic balance
Do:
• Check the effect of biasing the device in class B or C
by reducing the base voltage by 50 mV.
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
3
itest
RB
XOUT
Exc. 3: Measuring Zin
In pierce.i, a CMOS Pierce oscillator is characterized
by driving it by a 1-tone test current source and measuring the voltage that developes across port XOUT-XIN.
Oscillation criteria is that Zamp(Amp) = -Zresonator(f), so
Find
• excact oscillation amplitude if Re(Zreson) = 18 ohm.
• find Im(Zamp) at that point and note that it will pull
the resonance frequency.
XIN
Note that due to large RB the circuit settles slowly, and
similar amplitude sweep using transient analysis would
be very slow.
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
4
Exc. 4: Measuring IIP3
In mtanhiip3.i, both conventional and multi-tanh differential pair are measured using a 2-tone input signal.
The figures are in Chapter 6, when driven from 50 differential source.
1 1
1 1
• Run the same simulations when driven from 500
ohms
4 1
1 4
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
5
VOLTERRA TOOLS
Maple
Maple
.net
.mws
function
calls
• describe circuit topology with MNA matrix
• show the location of inputs
• list the control and output nodes of nonlinear components
rules
Matlab
Matlab
netlist
+sweeps
Volterra kernels can be analyzed symbolically using
Maple and numerically using Matlab. In both cases,
the following needs to be done:
nli_main
calculation
of
kernels
Calculation proceeds so that using linear response,
controlling voltages are calculated (in general they are
differential, e.g. v1[3]-v1[4] is voltage between nodes
3 and 4 at frequency w1), and usign them, 2nd order
currents in nonlinear components are calculated (gH2()
and cH2() in Maple).
These currents are now the 2nd order input vector for
the circuit, and their voltage response is calculated
using linear model t frequency w1+w2.
Then, using 1st and 2nd order controlling voltages, 3rd
order distortion currents are calculated, injected to the
circuit and voltage responses are calculated.
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
6
voltrules.txt for Maple:
restart;
with(linalg);
# initialisation
# nonlin 2nd order current of 1-dim. conductance
# v1,v2 are 1st order voltages at w1, w2
# KV is a vector containing K1,K2,K3
gH2 := proc(v1,v2,KV) ;
KV[2]*v1*v2;
end;
# nonlin 3rd order current of 1-dim. conductance
# v1,v2,v3 are 1st order voltages at w1, w2, w3
# v12, v13,... are 2nd order voltages at w1+w2,
# w1+w3, ...
gH3 := proc(v1,v2,v3,v12,v13,v23,KV) local t1,t2;
t1 := KV[3]*v1*v2*v3;
t2 := 2/3*KV[2]*(v1*v23 + v2*v13 + v3*v12);
evalm(t1+t2);
# matrix addition
end;
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
# nonlin 2nd order current of a 1-dim cap.
#
cH2 := proc(v1,v2,KV,w1,w2) ;
I*(w1+w2)*KV[2]*v1*v2;
end;
# nonlin 3rd order current of a 1-dim cap.
#
cH3 := proc(v1,v2,v3,v12,v13,v23,KV,w1,w2,w3)
local t1,t2;
t1 := K3*v1*v2*v3;
t2 := 2/3*K2*(v1*v23 + v2*v13 + v3*v12);
I*(w1+w2+w3)*(t1+t2);
end;
7
Iin
1
Exc. 5: Finding Volterra transfer function for amp
In gmramp.net, the amplifier on left is described. Current equations in nodes 1 and 2 are
2
+
-
1
-
1 ⋅ v 1 = I in
jωC ⋅ v 2 = – g mA ⋅ v 1 + g mB ⋅ ( – v 2 )
gmA
C
+
which in matrix form is
gmB
v
1
0
I
⋅ 1 = in
g mA ( g mB + jωC )
v2
0
Next, in voltrules.txt basic rules for Volterra kernels in
Maple are shown, and next, in gmramp.net, the circuit
and positions of distortion current sources are shown.
Do:
• derive 2nd order Volterra response
• modify gmramp.net such that the control and output
polarity of gmB are changed. It does not affect linear
transfer function but does affect distortion.
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
8
gmramp.net
## INV AMP: gm loaded by another gm and cap
#
# IV: input position, gmXv: K1, K2, K3 of cond. X
#
Iv := vector([ 1, 0]);
#linear input signal
gmAv := vector([ gmA, gmA*K2, gmA*K3]);
gmBv := vector([ gmB, gmB*K2, gmB*K3]);
# H1 calcs v vector for given current vector input Iin
H1 := proc(w,Iin) local Y;
# MNA admittance matrix
Y := matrix( [
[1,
0
], # node 1
[gmA , (gmB + I*w*C)] ]); # node 2
evalm( inverse(Y) &* Iin);
end;
H2 := proc(w1,w2)
local v1,v2,inA,inB,H2A,H2B;
v1 := H1(w1,Iv);
# 1st order voltage at w1
v2 := H1(w2,Iv);
# 1st order voltage at w2
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
# distortion currents and voltages caused by them
inA := gH2(v1[1],v2[1],gmAv); # calc current
H2A := H1(w1+w2,vector([0,-inA]));# inject it
inB := gH2(-v1[2],-v2[2],gmBv);
H2B := H1(w1+w2,vector([0,+inB]));
evalm(H2A + H2B);
end;
H3 := proc(w1,w2,w3)
local v1,v2,v3, v23,v13,v12,inA,inB,H2A,H2B;
v1 := H1(w1,Iv); v2 := H1(w2,Iv); # 1st order
v3 := H1(w3,Iv); v12 := H2(w1,w2);
v13 := H2(w1,w3); v23 := H2(w2,w3); # 2nd ord
# distortion currents and voltages caused by GA,GB
inA :=
gH3(v1[1],v2[1],v3[1],v12[1],v13[1],v23[1],gmAv);
H2A := H1(w1+w2+w3,vector([0,-inA]));
inB := gH3(-v1[2],-v2[2],-v3[2],-v12[2],-v13[2],v23[2],gmBv);
H2B := H1(w1+w2+w3,vector([0,+inB]));
evalm(H2A + H2B);
end;
9
1
Iin
Exc. 6: Finding Volterra for current mirror
In virtap.net, a current mirror on left is described.
Current equations in nodes 1 and 2 are
2
jωC ⋅ v 1 = I in – g mA ⋅ v 1
g o ⋅ v 2 = – g mB ⋅ v 1
+
+
-
-
gmA
C
gmB
go
which in matrix form is
( g mA + jωC ) 0
g mB
go
⋅
v1
v2
=
I in
0
Its description for Maple is shown on the next page.
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
10
virtap.net:
restart;
with(linalg);
# current mirror
# IV: input position, gmXv: K1, K2, K3 of cond. X
Iv := vector([ 1, 0]);
gmAv := vector([ gmA, gmA*K2, gmA*K3]);
gmBv := vector([ gmB, gmB*K2, gmB*K3]);
# H1: lin. voltage at w with input Iin
H1 := proc(w,Iin) local Y;
#
Y := matrix( [
[(gmA+I*w*C), 0],
# node 1
[ gmB
, g0] ]);
# node 2
evalm( inverse(Y) &* Iin); # solve voltage vect.
end;
H2 := proc(w1,w2)
local v1,v2,inA,inB,H2A,H2B;
v1 := H1(w1,Iv);
v2 := H1(w2,Iv);
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
# distortion currents and voltages caused by them
inA := gH2(v1[1],v2[1],gmAv);
H2A := H1(w1+w2,vector([-inA,0]));
inB := gH2(v1[1],v2[1],gmBv);
H2B := H1(w1+w2,vector([0,-inB]));
evalm(H2A + H2B);
end;
H3 := proc(w1,w2,w3)
local v1,v2,v3, v23,v13,v12,inA,inB,H2A,H2B;
v1 := H1(w1,Iv); v2 := H1(w2,Iv);
v3 := H1(w3,Iv); v12 := H2(w1,w2);
v13 := H2(w1,w3); v23 := H2(w2,w3);
# distortion currs and voltages caused by M1,M2
inA :=
gH3(v1[1],v2[1],v3[1],v12[1],v13[1],v23[1],gmAv);
H2A := H1(w1+w2+w3,vector([-inA,0]));
inB :=
gH3(v1[1],v2[1],v3[1],v12[1],v13[1],v23[1],gmBv);
H2B := H1(w1+w2+w3,vector([0,-inB]));
evalm(H2A + H2B);
end;