Exc. 1: Hartley mixer Hartley mixer cancells the image ... - Oulu

RF LO + IF
90 -
90
signal image
RF
LO
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
Exc. 1: Hartley mixer
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
Do:
• select lower sideband
• select upper sideband
• check the effect of 10% error in LO phase shift
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.
1
2

itest
XIN
RB
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
1 1 1 1
4 1 1 4
XOUT
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
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.
Note that due to large RB the circuit settles slowly, and
similar amplitude sweep using transient analysis would
be very slow.
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.
• Run the same simulations when driven from 500
ohms
3
4

Maple
.net
rules
Matlab
.mws
function
calls
netlist nli_main
+sweeps
calculation
of
kernels
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
voltrules.txt for Maple:
restart;
with(linalg); # initialisation
Maple
Matlab
# 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
VOLTERRA TOOLS
Volterra kernels can be analyzed symbolically using
Maple and numerically using Matlab. In both cases,
the following needs to be done:
• describe circuit topology with MNA matrix
• show the location of inputs
• list the control and output nodes of nonlinear components
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.
# 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;
5
6

I in 1
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
gmramp.net
1
+
-
g mA
## 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]);
2
C
g mB
# 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
-
+
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
1 ⋅ v1 = Iin jωC ⋅ v2 = – gmA ⋅ v1 + gmB ⋅ ( – v2) which in matrix form is
1 0 v1 ⋅
gmA ( gmB + jωC ) v2 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 g mB are changed. It does not affect linear
transfer function but does affect distortion.
# 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;
=
I in
0
7
8

I in
(C) 1999- Timo Rahkonen, University of Oulu, Oulu, Finland
virtap.net:
+
-
1
-
gmA C gmB go
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
+
2
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
jωC ⋅ v1 = Iin – gmA ⋅ v1 go ⋅ v2 which in matrix form is
= – gmB ⋅ v1 ( gmA + jωC ) 0
g mB
Its description for Maple is shown on the next page.
g o
# 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;
⋅
v 1
v 2
=
I in
0
9
10