Radio Frequency Integrated Circuit Design - Webs

R E = re� v IP3
2vT� 2/3
LNA Design
546 mV
− re = 5��2 � 25 mV� 2/3
− 5� = 19.6�
This is a rough estimate for what the linearity should be. Also, there are
many other factors that can limit the linearity of the circuit. We will start with
R E = 20�.
The gain can also be found now. Knowing that we want 12 dB of voltage
gain means a gain of 4 V/V. We will assume that the buffer has a voltage gain
A BO of about 0.9 (they will always have a bit of loss). Thus, the load resistance
can be obtained:
G =
R L
A
R E + re
BO ⇒ R L = G
(R
A E + re ) =
BO
4
(20� + 5�) ≈ 115�
0.9
Now we need to set the feedback resistor. Knowing that the input impedance
needs to be 75� (we approximate that the input impedance is R f divided
by the gain),
Z in ≈
R f
R L
R E + re
⇒ R f = Z inRL
R E + r e
= 75� �115�
20� + 5�
= 345�
The other thing that must be set is the value of C f . Since the LNA must
operate down to 50 MHz, this capacitor will have to be fairly large. At 50
MHz, if it has an impedance that is 1/20th of R f , then this would make it
approximately 50 pF. We will start with this value. It can be refined in simulation
later.
The only thing left to do in this example is to size the transistors. With
all the feedback around this design, the transistors will have a much smaller
bearing on the noise figure than in a tuned LNA. Thus, we will make the input
transistor fairly large (60 �m) and the other two transistors will be sized to be
30 �m fairly arbitrarily. Having high f T is important, but in a 50-GHz process,
this will probably not be an issue. The other last detail that needs to be addressed
is the bias level at the base of Q 2. Given that the emitter of Q 1 is at 100 mV,
the base will have to sit at about 1V. The collector of Q 1 should be higher
than this, for example, about 1.2V. This means that the base of Q 2 will need
to be at about 2.2V, and since its collector will sit at about 2.7V, this transistor
will have plenty of headroom.
The noise figure of this design can now be estimated. First, the noise
voltage produced by the source resistance is
191