176 LNA Designand 1cPb» - (7.16) 2Pb» - (7.17)Example 7.5: Calculation of Poles and Zeros with Simplified ExpressionsWith the expression as above, the poles occur at 2.60 GHz and 120.94 GHz, which are reasonably close to the exact values.7.1.3 The Common-Base/Gate Amplifier (Cascode)The common-base (or common-gate) amplifier is often combined with the common- emitter (or common-source) amplifier to form an LNA. It can be used by itself as well. Since it has low input impedance, when it is driven from a current source, it can pass current through it with a near unity gain up to a very high frequency. Therefore, with appropriate choice of impedance levels, it can also provide voltage gain. The small-signal model for the common-base amplifier is shown in Figure 7.4 (ignoring the transistor’s output impedance). The analysis for a common-gate am-plifier would be identical, except for the change of names, and with no equivalent for rp.The current gain (ignoring Cm and ro) for this stage can be found to be: outin1111eiij C rj»»++ (7.18)where ωT = 2pfT (see (7.10)). At frequencies below ωT, the current gain for the stage is 1. Note that the pole in this equation is usually at a much higher frequency than the one in the common-emitter amplifier, since re < rb + Rs. As mentioned above, the input impedance of this stage is low and is equal to 1/gm at low frequencies. At the pole frequency, the capacitor will start to dominate and the impedance will drop.This amplifier can be used in combination with the common-emitter amplifier (discussed in Section 7.1.1) to form a cascode LNA as shown in Figure 7.5. In this Figure 7.4 Small signal model for the common-base amplifier.