Using an fTDoubler Amplifier for a High GainBandwidth Product
Key Takeaways

Transistors used in an amplifier come with a unity gain cutoff frequency, designated as f_{T}.

An f_{T}doubler amplifier doubles the f_{T} characteristics of an amplifier and provides a high gainbandwidth product.

The input current supplied to a differential amplifier becomes twice the output current when there is an f_{T} doubler stage.
High bandwidth and high gain are difficult to achieve in conventional amplifiers
High bandwidth is an essential requirement of highfrequency transistor amplifiers—achieving high bandwidth in highfrequency applications without compromising amplifier gain is required. However, this need can prove problematic.
The gain of a transistor amplifier is dependent on the input signal’s frequency—the gain is highest when the input frequency is lowest. As the input frequency increases, the amplifier gain drastically decreases until it reaches unity gain cutoff frequency, which is designated as f_{T}. Transistors, or any bipolar device, employed in the amplifier come with f_{T}, which is the frequency at which the gain of the amplifier is unity. At this frequency, the amplifier is not capable of providing any gain. This is one limitation hampering the improvement of bandwidth and gain in amplifiers.
There are several solutions for mitigating this problem in amplifiers, including using emitterfollower buffers, resistive feedback, peaking with LC networks, or f_{T}doubler cells. The f_{T}doubler amplifier, also known as a current doubler, is one solution, as it doubles the f_{T} characteristics of the amplifier and provides a high gainbandwidth product.
The fTdoubler Amplifier
The fT doubler amplifier improves fT characteristics
The f_{T} is the index that represents the ability of the amplifier to offer a combination of current gain and bandwidth. There is always a tradeoff between bandwidth and gain. The f_{T} doubler amplifier provides more room for making this tradeoff by increasing the unity gain cutoff frequency.
The figure above shows the f_{T}doubler differential amplifier with four bipolar transistors: Q_{1}, Q_{2}, Q_{3}, and Q_{4}. The base terminals of Q_{3} and Q_{4} are connected to a commonmode voltage. Differential input voltages are given at terminals In1 and In2.
The f_{T}doubling is achieved by doubling the current gain when compared to conventional differential amplifiers. The input current supplied to a differential amplifier becomes twice the output current when there is an f_{T} doubler stage. It doubles the current, which, in turn, doubles the unity gain cutoff frequency.
The differential amplifier with and without an f_{T}doubler cell has the same break frequency, however, the f_{T}doubler amplifier is twice that of the simple differential amplifier. The figure below shows the current gain versus frequency plot of the f_{T}doubler amplifier and the differential amplifier.
The fT doubler amplifier fT is greater than that of the differential amplifier
The SmallSignal Model of the fTDoubler Amplifier
The highfrequency behavior of the f_{T}doubler differential circuit can be studied and analyzed using the smallsignal model. As the circuit of the f_{T}doubler amplifier is symmetrical, one half of the circuit needs to be analyzed for a complete circuit behavioral study. A hybrid, pimodelbased smallsignal circuit of the f_{T}doubler amplifier is derived for circuit behavioral studies. The figure below shows the smallsignal model of the f_{T}doubler amplifier.
The fT  doubler amplifier smallsignal model is useful in frequency analysis
By combining the voltagedependent current sources and lumping together the impedances, the smallsignal model can be further reduced to the equivalent circuit (a), as given in the figure below. The Miller transformation simplifies the equivalent circuit, and we obtain the hybridpi topology of a bipolar transistor amplifier with a doubled current gain.
The Miller transformation is used to simplify the equivalent circuit to hybridpi topology
The frequency range of amplifiers in RF and microwave applications is currently hitting the upper limit. The need for high performance, high gain amplifiers have led to the incorporation of f_{T}doubler amplifiers in RF circuits. These amplifiers emphasize gain improvement and maintain a good gainbandwidth product.
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