Copyright © 2011 by Wayne Stegall
Updated March 3, 2012. See Document History at end for
details.
Cascode Phono Preamplifiers
SPICE
verified.
Capacitively
coupled
cascode
enables
an
easily
adjustable
singlestage
preamp.
Introduction
Investigation of a preamp illustrating a lownoise application of the
inverting RIAA equalization circuit lead to this discrete preamp
design. Although it appears to be a two stage circuit with a
buffer, the second stage is only a cascode to the first stage, creating
a virtual onestage design. Separating the classa input from the
cascode with a capacitor enables separate biasing for each. Thus
the cascode can have a lower current bias than the input enabling the
necessary gain from one stage without excessively high voltage
supplies. A direct cascode design would require a power supply in
excess of 200V. I investigated two variations on the circuit that
did not produce results as good as this one. One was a direct
cascode with a shunt resistor around the cascode to the positive supply
to reduce cascode bias, resulting in higher distortion. The other
was a direct cascode with a shunt current source around the cascode to
the positive supply to reduce cascode bias, resulting in lower
distortion with higher noise. Both of these had more sensitive
and difficult to adjust bias issues. This one turned out simpler
in the end.
Discrete Circuit
Figure
1:
Schematic
of
Passive
Cascode
Phono
Preamplifier


Parts List





R_{i}^{1}

47kΩ 

C_{1NB}^{4} 
2.2nF 1% 
C_{i}^{1} 
25pF


R_{2N} 
2.61kΩ 1% 
Q_{1}Q_{8}

LSK170A nchannel jfet


C_{2NA}^{4} 
39nF 1% 
R_{1}R_{8} 
27.4Ω


C_{2NB}^{4} 
3.3nF 1% 
R_{9}^{2} 
750Ω 5% 

Q_{10},Q_{11} 
LSK170C nchannel jfet 
C_{1} 
2200µF electrolytic 

R_{11} 
75Ω 5% 
Q_{9} 
2N3904 small signal NPN^{3}


C_{2} 
100µF electrolytic

R_{10} 
13kΩ 5%


R_{12} 
1kΩ 5% 
R_{1N} 
18.2kΩ 1%


R_{13} 
100kΩ 5% 
C_{1NA}^{4} 
120nF 1% 




Notes:
^{1}Values calculated for
your
cartidge can be substituted for default values shown.
^{2}The actual hardware circuit may require hand choosing
R_{9} for the correct V_{D} bias due to JFET parameter
variations.
^{3}SPICE simulation showed no significant noise
improvement by upgrading to an ultralow noise BJT (i.e. MAT02) because
gain falls entirely to input stage.
^{4}AB capacitor pairs are connected together in
parallel. 
Initial Design Decisions
Choose +30V supplies for VDD and VCC. choose 15V supply for
VEE.
Want gain of 46dB at 1kHz to amplify 5mV to 1V
_{rms}.
Design
Transconductance Frontend Design
It is desirable
to choose source resistors small enough to make their noise
contribution insignificant compared to the JFET to lower
noise.
(1)

Resistor
noise
equation
(per
√Hz, figure of merit,
does not account for
bandwidth)



Rearrange resistor noise equation to calculate equivalent input noise
resistance of JFET.
(2)

R =

v_{nresistorrtHz}^{2}
4kT

=

1nV^{2}
4 x 1.3806504e23 x 298.15ºK 
= 60.7325Ω 
Choose 27Ω source resistors on the chance that lower values will be
acceptable. This presumes averaging among eight parallel devices
will greatly stablize average transistor parameters. Choose
nearest 1% value to allow use of metalfilm resistors.
R_{1}R_{8}
= 27.4Ω
Figure 2: LSK170A SPICE
model for
reference 
.MODEL LSK170A NJF
+ BETA = 0.0378643
VTO = 0.4025156 LAMBDA
= 4.783719E3
+ IS =
3.55773E14
+ RD =
10.6565
RS =
6.8790487
+ CGD =
3.99E11
CGS =
4.06518E11
+ PB =
0.981382
FC =
0.5
+ KF =
0
AF
=
1

It is possible to calculate a gate voltage bias from a drain current
specification, but
iteration (repetitive computer calculations) or a load line graph are
required to calculate the current bias from a specified gate voltage
bias. To begin small signal analysis
from the
parameters given (V
_{GS} = 0V and R
_{S} = 27.4Ω), get
current bias from preliminary SPICE deck.
SPICE shows a combined drain current of 26.3811mA. Individual
drain
current then calculates to 3.29764mA.
Calculate JFET transconductance:
(3)

g_{fs}
= 2 × 

= 2 × 

37.8643mA/V^{2} x
3.29764mA 

= 22.3484mS

Calculate transconductance of individual parallel elements then of
entire circuit frontend:
(4)

g_{fscktelement} =

1
R_{S} + 1/g_{fs}

=

1
27.4Ω + 1/22.3484mS 
= 13.8608mS

(5)

g_{fsfrontend} =
8 × 13.8608mS = 110.886mS 
Because this stage will drive a cascode through C
_{1}, there
will be only a trace of AC at V
_{D} and therefore no headroom
requirement. Because higher values of R
_{9} and R
_{10}
will lower distortion as regards the ac impedance seen by the emitter
of Q
_{9}, choose V
_{D} bias at 10V to maximize R
_{9},
and
calculate
R
_{9}.
(6)

R_{9} =

V_{DD  }V_{D}
I_{DTOTAL} 
=

30V  10V
26.3811mA 
= 758.119Ω 
Round to nearest 5% value:
R_{9} = 750Ω
Calculate C
_{1} for a pole of 0.1Hz
(7)

C_{2} =

1
2π × R_{9} × f_{hp} 
=

1
2π × 750Ω × 0.1Hz 
= 2.12207mF 
Round up to nearest 20% value:
C_{2} = 2200µF
Cascode Design
Calculate DC gain for the desired 46dB gain at 1kHz.
(8)

A_{VDC} = 9.89808 × A_{V1kHz}
= 9.89808 × 200V/V = 1979.62V/V 
Given A
_{VDC} = g
_{fsfrontend} × R
_{1N}
calculate R
_{1N} for chosen gain.
(9)

R_{1N} =

A_{VDC}
g_{fsfrontend}

=

1979.62V/V
110.886mS 
= 17.8527kΩ 
Reserve final choice of R
_{1N} for adjustments below.
R
_{10} has two effects on distortion: As pertains to
bias, lowering R
_{10} will lower distortion by increasing the
bias. As pertains to ac impedance, the parallel of R
_{9}
and R
_{10} lower distortion as they are raised. Because R
_{9}
is much lower than the expected R
_{10}, prefer to choose R
_{10}
to increase bias relative to other factors. Choose V
_{C}
bias at 10V as a compromise between a low R
_{10} and
reasonable headroom, and calculate R
_{10}.
(10)

R_{10} =

R_{1N} × V_{R10}
V_{R1N} 
=

17.8527kΩ(0.7V  15V)
(30V  10V) 
= 12.7647kΩ 
Round to nearest 5% value:
R_{10} = 13kΩ
Output Buffer Design
The choice of JFET in the output buffer stage is not
critical. As for noise the gain stages have amplified their noise
enough
to make that of the output less critical. Consider that 1nV/√Hz
amplified by about 100 gain at 1kHz is 100nV/√Hz. A common
2N3819 would be a good choice as would others in this respect. It
is better to prioritize the maximization of g
_{fs} in order to
reduce buffer stage distortion. To this end, an LSK170 would be a
best known choice due to high k
_{n} and g
_{fs}, with
the lowest possible noise for a bonus. Since
you
would
be
faced
with
component
variations
on
a
part
of
your
own
choice,
I
suggest
you
choose
a
value
of R
_{11} by trial and error to get a bias current
within your JFETs specifications. You should not match Q
_{10}
and Q
_{11}. Rather, because Q
_{10} will operate
freer if
it is not pushed to its current limit, you should choose Q
_{10}
to have a higher g
_{fs} than Q
_{11}. To this end,
try both transistors in the Q
_{11} position and place the one
there that gives the lowest bias current through Q
_{11}.
Since this aspect is experimental, calculating R
_{11} may be
overengineering. A R
_{11} corresponding to the JFET's
rated g
_{fs} would be a good starting point for a midpoint
bias, i.e.:
(11)

R_{11} =

1
g_{fs} 
=

1
10mS 
= 50Ω 
or alternatively setting R
_{S} to ratio of cutoff voltage to
maximum current for another approximate midpoint bias:
(12)

R_{11} =

V_{T}
I_{DSS} 
=

2V
20mA 
= 100Ω 
If you must make an exact calculation from a chosen I
_{D}, the
following was derived from the FET equation by circuit analysis:
(13)

R_{S} =

V_{T}
 sqrt(I_{D}/k_{n})
I_{D} 
Choose R
_{11} =
75Ω as
median of two estimates.
Choose R12 output limiter for worst case of 10mA maximum gate current
and 20mA maximum drain current.
(14)

R_{12} =

VCC
I_{SMAX} 
=

30V
30mA 
= 1kΩ 
Calculate output coupling capacitor to give 1Hz highpass pole with a
600Ω load knowing that the pole frequency will be much lower with a
more reasonable load of 10kΩ:
(15)

C_{2} =

1
2π × R_{LMIN} × f_{hp} 
=

1
2π × (1kΩ + 600Ω) × 1Hz 
= 99.4718µF 
Round up to next standard value C
_{3} =
100µF
RIAA Analysis
Because the preliminary SPICE deck produced excellent frequency
response, I left stray impedances out of the calculations.
These calculations are carried out according to the document
Phono Equalization Calculations:
Passive RIAA Network.
Given R
_{1N} = 17.8527kΩ, Calculate R
_{2N}.
(16)

R_{2N} =

R_{1N}
6.877358491 
=

17.8527kΩ
6.877358491 
= 2.59587kΩ 
Calculate C
_{1N} and C
_{2N} from R
_{1N}.
(17)

C_{1N} =

2187µs
R_{1N} 
=

2187µs
17.8527kΩ 
= 122.502nF 
(18)

C_{2N} =

750µs
R_{1N} 
=

750µs
17.8527kΩ 
= 42.0105nF 
These equalization calculations produce the following plot in SPICE
where the
response is down to 0.578dB at 20kHz after a 0.07dB rise in the
midrange.
Figure
3:
SPICE
Bode
Plot
of
Discrete
Circuit
with
Initial
Values


SPICE deck for discrete
circuit with inital values.
Supporting models:
lsk170.txt,
models1.txt,
mat02_03.txt,
invriaa2.txt.
Adjustments to Discrete Circuit
Standard value component choices produce the following plot where the
response trends generally down to 0.784dB at 20kHz. The standard
values producing this response are logged in the parts list above.
Figure
4:
SPICE
Bode
Plot
of
Discrete
Circuit
after
Standard
Value
Choices


The actual hardware circuit may require hand choosing R
_{9} for
the correct V
_{D} bias due to JFET parameter variations.
The bias on the cascode will not require adjustment because BJT
voltage bias is accurately predictable.
SPICE deck for
discrete circuit with standard value choices.
Supporting models:
lsk170.txt,
models1.txt,
mat02_03.txt,
invriaa2.txt.
Other Spice Results
S/N ratio is 104.415dB relative to 1V
_{RMS} output.
Add 4.71685dB for gain over RIAA for normalized S/N of 109.13185dB
Fourier analysis for vout is dominated by second harmonic:
No. Harmonics: 16, THD: 0.552496 %, Gridsize: 1024,
Interpolation Degree: 3
Harmonic 
Frequency 
Magnitude 
Norm.Mag 
Percent 
Decibels 






1 
1000 
1.24009 
1 
100 
0 
2 
2000 
0.00656276 
0.00529215 
0.529215 
45.52735709 
3 
3000 
0.00151543 
0.00122202 
0.122202 
58.25843372 
4 
4000 
0.00079421 
0.000640444 
0.0640444 
63.87037677 
5 
5000 
0.000486011 
0.000391915 
0.0391915 
68.13616228 
6 
6000 
0.00040426 
0.000325991 
0.0325991 
69.7358878 
7 
7000 
0.00035357 
0.000285115 
0.0285115 
70.89959867 
8 
8000 
0.000310044 
0.000250016 
0.0250016 
72.04064395 
9 
9000 
0.000275186 
0.000221908 
0.0221908 
73.07654081 
10 
10000 
0.000247239 
0.000199371 
0.0199371 
74.00676026 
11 
11000 
0.000225024 
0.000181457 
0.0181457 
74.82452547 
12 
12000 
0.000206485 
0.000166508 
0.0166508 
75.57129791 
13 
13000 
0.000190323 
0.000153475 
0.0153475 
76.27924716 
14 
14000 
0.000176728 
0.000142512 
0.0142512 
76.9229713 
15 
15000 
0.000165178 
0.000133198 
0.0133198 
77.51004592 
I expect that gain change with frequency will change the way
preequalization and postequalization transfer curves juxtapose to
create the final transfer curve. Therefore transfer error curve
analysis is given for three frequency ranges:
Figure
x:
Transfer
curve
error at DC50Hz

Figure
x:
Transfer
curve
error at 1kHz 
Figure
x:
Transfer
curve
error at 21kHz 



I initally attributed an incorrect cause to the fact that all of these
curves have a bend direction opposite that of the
hybrid circuit because I falsely presumed the hybrid circuit to be
inverting as the discrete one. Now I attribute it to this
discrepancy.
Hybrid Circuit
Figure
5:
Schematic
of
Hybrid
Cascode
Phono
Preamplifier


Parts List





R_{i}^{1}

47kΩ 

R_{1N} 
16.5kΩ 1% 
C_{i}^{1} 
25pF


C_{1NA}^{3} 
180nF 1% 
Q_{1}Q_{8}

LSK170A nchannel jfet


C_{1NB}^{3} 
13nF 1% 
R_{1}R_{8} 
27.4Ω


R_{2N} 
1.4kΩ 1% 
R_{9}^{2} 
750Ω 5% 

C_{2NA}^{3} 
51nF 1% 
C_{1} 
2200µF electrolytic 

C_{2NB}^{3} 
2.7nF 1% 
U_{1} 
OPA227 operational amplifier





Notes:
^{1}Values calculated for
your
cartidge can be substituted for default values shown.
^{2}The actual hardware circuit may require hand choosing
R_{9} for the correct V_{D} bias due to JFET parameter
variations.
^{3}AB capacitor pairs are connected together
in
parallel. 
This is the circuit that inspired the one above.
Initial Design Decisions
Choose +30V supply for VDD, +15V supply for VCC, and 15V supply for
VEE.
Want gain of 46dB at 1kHz to amplify 5mV to 1V
_{rms}.
Transconductance Frontend Design
This circuit has the same frontend design as the discrete
version. It is only necessary to carry forward the resistance
calculated for R
_{1N} in the discrete circuit as the DC
impedance of the inverting RIAA network used here and do the RIAA
Analysis.
RIAA Analysis
These calculations are carried out according to the document
Phono Equalization Calculations:
Inverting RIAA Network.
Given R
_{1N} + R
_{2N} = 17.8527kΩ, Calculate R
_{1N}
and R
_{2N}.
(19)

R_{1N} = 
17.8527kΩ × 11.7778
12.7778

= 16.4556kΩ 
(20)

R_{2N} = 
17.8527kΩ × 1
12.7778

= 1.39717kΩ 
(21)

C_{1N} = 
T_{P1}
R_{1N} 
=

3180µs
16.4556kΩ 
= 193.247nF

(22)

C_{2N} = 
T_{P2}
R_{2N} 
=

75µs
1.39717kΩ 
= 53.6799nF

These equalization calculations produce the following plot in SPICE
where the
response is flat until down to 0.637dB at 20kHz
Figure
6:
SPICE
Bode
Plot
of
Hybrid
Circuit
with
Initial
Values


SPICE deck for hybrid
circuit with inital values.
Supporting models:
lsk170.txt,
OPA227.txt,
AD797AN.txt,
invriaa2.txt.
Adjustments to Hybrid Circuit
Because this circuit places its operational amplifier after firststage
transconductance gain, it seemed that it would not require an
ultralownoise operational amplifier such as an AD797 or a
NME49990. After simulating SPICE an AD797 with an ultralow noise
spec of 0.9nV/√Hz as a baseline, I first tried an AD825 with an
ordinary noise spec of 12nV/√Hz as an alternative because of its 10kHz
dominant pole. This combination lost the circuit 1dB of SNR
compared to the AD797. I then tried an OPA227 with a low noise
spec of 3nV/√Hz as a compromise. Because it simulated essentially
the same noise results as the AD797, I chose it as a more cost
effective alternative.
Standard value component choices produce the following plot where the
response is flat until down to 0.657dB at 20kHz. The standard
values producing this response are logged in the parts list above.
Figure
6:
SPICE
Bode
Plot
of
Hybrid
Circuit
after
Standard
Value
Choices


SPICE deck for hybrid
circuit with standard value choices.
Supporting models:
lsk170.txt,
OPA227.txt,
AD797AN.txt,
invriaa2.txt.
Other Spice Results
S/N ratio is 1.03896dB relative to 1V
_{RMS} output.
Add 5.1915dB for gain over RIAA for normalized S/N of 109.088dB
Fourier analysis for vout:
No. Harmonics: 16, THD: 0.148538 %, Gridsize: 1024,
Interpolation Degree: 3
Harmonic 
Frequency 
Magnitude 
Norm.Mag 
Percent 
Decibels 






1 
1000 
1.30842 
1 
100 
0 
2 
2000 
0.00100123 
0.000765218 
0.0765218 
62.32429645 
3 
3000 
0.000961284 
0.00073469 
0.073469 
62.67791743 
4 
4000 
0.000729173 
0.000557292 
0.0557292 
65.07834383 
5 
5000 
0.000576157 
0.000440345 
0.0440345 
67.12413861 
6 
6000 
0.000485056 
0.000370719 
0.0370719 
68.6191031 
7 
7000 
0.000413432 
0.000315978 
0.0315978 
70.00686308 
8 
8000 
0.000363602 
0.000277894 
0.0277894 
71.1224166 
9 
9000 
0.000322851 
0.000246748 
0.0246748 
72.15492718 
10 
10000 
0.000291564 
0.000222837 
0.0222837 
73.04025394 
11 
11000 
0.000264078 
0.00020183 
0.020183 
73.9002856 
12 
12000 
0.00024286 
0.000185613 
0.0185613 
74.6278322 
13 
13000 
0.000223275 
0.000170645 
0.0170645 
75.35812865 
14 
14000 
0.000207823 
0.000158835 
0.0158835 
75.98107585 
15 
15000 
0.000194001 
0.000148271 
0.0148271 
76.57887567 
For now I presume that preequalization transfer curve of the JFET front
end dominates due to the seemingly vanishing distortion specification
of the operational amplifier. Therefore I expect that the low
frequency transfer error curve will suffice for the entire audio band:
Figure
x:
Transfer
curve
error at DC50Hz 

Document History
May 3, 2011 Created.
May 4, 2011 Added missing × symbol in equation (5), reformatted
equation (1), update figure 5 schematic and revised explanation of R_{10}
choice preceding equation (10).
May 6, 2011 Completed hybrid design promised for second circuit.
May 6, 2011 Updated SPICE decks to replace any unchanged
preliminary
values with correct calculated ones. The differences were not
ones expected to change the results.
May 10, 2011 Corrected two grammar and spelling faults.
May 20, 2011 Improved SPICE decks to reduce interpolation noise
in fourier results.
March 3, 2012 Added transfer error curve analysis for both
circuits. Corrected incorrect interpretation of inverted transfer
error curve bend direction between circuits.