Microwave Bipolar Transistor:
The micro wave bipolar transistor is a non linear device, which is mostly silicon npn type operating up to ‘5 GHz’. The geometry of the transistor can be characterized as interdigitated geometry, over lay geometry and matrix geometry. These geometries have wide emitter area to overcome transit time limitations. The interdigitated geometry is used for small signal, small power circuits. The over lay and matrix types are used for small power only. For high frequency applications, the NPN structure is preferred because the electron mobility is higher than hole mobility. Diffusion and ion implantation are the common methods used for transistor fabrication.
Basic Construction:
An epitaxial n layer is grown over a low resistivity n+ silicon substrate above the epitaxial layer a p region is diffused forming the base and n+ layer is diffused over the p region to form the emitter. The silicon substrate acts as the collector.
The microwave bipolar transistors are active three terminal devices which is commonly used for amplification process and switching phenomena. The three regions of the transistor are emitter, base and collector. The emitter region forms the input of the device and the collector region forms the output of the device. The emitter region of the transistor is heavily doped and has moderate area of cross section. The base of the transistor is thin and lightly doped to reduce the recombination rate. The collector region of the transistor is large and moderately doped. The charge carriers from the emitter are supplied to the collector through the base. When the charge carriers from the emitter reach the base some of them recombine with the charge carriers in the base. The remaining charge carriers are directed towards the collector constituting the collector current or output current.
Modes of Operation:
The microwave transistors have four modes of operation depending on the polarity of the applied voltage.
1. Normal Mode: In this mode, the emitter base junction of the npn transistor is forward biased and collector base junction is reverse biased. Most transistor amplifiers is operated in normal mode.
2. Saturation Mode: When both the emitter base junction and collector base junction are forward biased, the transistor is in saturation mode with low resistance and acts like a short circuit.
3. Cut Off Mode: When both the Tr junctions are reverse biased, the Tr is operated in Cut Off mode. The Tr acts like an open circuit. Both the saturation and cut off modes are used when transistor acts as a switch.
4. Inverted Active Mode: In this mode, the emitter base junction is reverse biased and collector base junction is forward biased.
Power Frequency Limitations:
Microwave transistors have limitations on frequency and power. These limitations can be due to maximum velocity of carriers, maximum electric field and maximum current. The four basic equations for the power frequency limitation are
1. Voltage – Frequency limitation:
VmfT = EmVs/2 π
Where, fT - Cut off frequency
fT = 1/2 πτ
τ = L/V
Vm - maximum voltage
Vs – velocity
Em – Maximum electric field
When the length decreases, the average time, τ decreases. As a result, the frequency increases. When the frequency increases, the applied max voltage decreases.
2. Current frequency Limitation:
Im XcfT = EmVs/2 π
Where, Xc – impedence
Im – Max Current
If the impedence level is zero, the maximum current is infinite. The impedance value should be maintained in such a way, that maximum current is obtained for producing maximum power.
3. Power - frequency Limitation:
√(Pm Xc)fT = EmVs/2 π
If the value of Xc is zero, the maximum power delivered is infinite.
4. Power Gain frequency Limitation:
√(Gm Vm Vth)fT = EmVs/2 π
Gm – Maximum Gain
Vm –Voltage
Vth – Thermal Voltage
If the frequency increases, the gain of the device decreases.
Equivalent Model of Microwave Bipolar Transistor:
Hybrid Pi equivalent model is commonly used in normal active mode for small signal operations.
A change of emitter voltage Vbe at the input terminal will induce a change of collector current at the output terminal. The mutual conductance or transconductance for the small signal model is given by,
gm = ∂ic/ ∂Vbe ------------- (1)
The density of charge carriers across the junction is given by,
np(0) = npoeVbe/VT ----------------- (2)
The collector current is defined based on the charge density as
ic = qADnnp(o) --------------- (3)
where, q – charge
A – Area of Cross Section
Dn – Diffusion constant
np(0) – Charge density
Substitute, eq (2) in eq (3)
ic = (qADn npoeVbe/VT)/Ln ---------------- (4)
Therefore, gm = ∂ic/ ∂Vbe
gm = qADn npoeVbe/VT)/LnVT
= qADn npo/LnVT
gm = ic/VT ------------------- (5)
Diffusion Capacitance:
Cbe = dQb/dVbe
Where, Qb - charge stored in the base.
Qb = qnp(o)ωbA/2
Sub for np(o) from (2)
Qb = qnpoeVbe/VTωbA/2
Therefore,
Cbe = qωbAnpoeVbe/VT/2VT
Cbe = qωbAnpo/2VT
From equation (3)
Cbe = icLnωb/2VTDn
From equation (5)
Cbe = gmLnωb/2Dn
If Ln = ωb
Cbe = gmωb2/2Dn
The input conductance,
gb = ic/hfe VT
gb = gm/hfe
where, hfe – input resistance/Forward emitter resistance