# Design of a Fixed IF Down-Conversion Double-Balanced Mixer for UHF Band Applications
## 4 Simulation and Experimental Results
### Double-Balanced Down-Conversion Mixer Noise Calculation and Simulation
#### 4.2.2 Noise Due to LO Switching Pair  
The local oscillator switching causes the Mixer noise, which is classified as direct switching noise and indirect switching noise. (i). Direct Switching Noise  
Additional 1/f noise, a weak signal overlapped on the LO switching signal, is experienced by the base. Significant changes in the LO signal cause the switching events to occur either forward or backward in time. As a result, the noise causes jitter. Understanding the difference between the switched current with and without jitter is necessary in order to quantify the noise contribution, as illustrated in Figure 13. Subtracting the two signals results in a sequence of pulses with the following properties:  
* The pulses are located at the edges of switching times. * The amplitude can be positive or negative, equal to twice the switched current. * The pulse width \(\Delta t=\frac{V_{n}(t)}{5}\), where \(V_{n}(t)\) is the magnitude of the base noise voltage at the time of switching and S is the slope of the LO voltage applied to the base. Figure 14 shows the relationship. The sampling frequency is double the LO frequency due to jitter happening at each switching moment or twice during each LO period (a pulse rate of pulse train \(2f_{LO}\)). Consequently, the normalized jitter noise current for one period is as follows:  
\[I_{o,n}=\frac{2}{T_{LO}}.2I_{RF}.\frac{V_{n}}{S} \tag{14}\]  
The slope (S) of the sinusoidal LO signal can be given as follows:  
Figure 12: The noise spectral content of the LO frequency and its harmonics down-converted to an IF port in the single-balanced mixer [26]. For a differential LO signal, \(V_{L}a{d}=2 sin\omega_{LO}t\); therefore, \(S=\frac{dV_{LO}d}{dt}=2V_{LO}\omega_{LO}\). So, \(ST_{LO}\) will be \(4\pi V_{LO}\). The baseband noise spectrum becomes the following:  
\[I_{o,n}(f)=\frac{1}{\pi V_{LO}}.I_{RF}.\ V_{n}(f) \tag{15}\]  
The noise \(V_{n}(t)\) from the LO switch is only transferred to the output during the zero crossing. Both switches contribute noise to the mixer output when they are on; no noise is  
Figure 14: (**a**) Ideal LO base voltage (solid line) and 1/f noise voltage (dashed line); (**b**) actual (solid line) and ideal (dotted line) LO base voltage; and (**c**) the time-offset (jitter) at a zero crossing, calculated from the noise voltage and the slope of the LO signal [18]. Figure 13: Direct switching noise: The LO signal with jitter can be understood as an undisturbed signal superimposed with a pulse train [18]. contributed when one switch is off, and when the other switch is on, it also contributes no noise due to its functioning as a cascade structure with a fixed tail current of \(I_{RF}\) by the RF input transconductance stage. The noise current at the mixer output is a series of pulses occurring at twice the LO frequency rate, with a height equal to \(2I_{RF}/S\), and a width that is randomly modulated by noise. The input noise is stationary and white, and its power spectral density is given by the following:  
\[\overline{V_{n,s}^{2}}=4 KT\bigg{(}r_{b2}+\frac{1}{2g_{m2}}\bigg{)} \tag{16}\]  
\[[g_{m2}]_{\text{ }zercrossing}=\frac{2I_{RF}}{\Delta V} \tag{17}\]  
where \(g_{m2}\) is the switch transconductance at zero crossing. The power spectral density of the output noise current is given by  
\[\overline{I_{n0,s}^{2}}=\int_{o}^{T_{LO}}p^{2}(t)\overline{V_{n,s}^{2}}=\bigg{(} \frac{2}{T_{LO}}\bigg{)}\bigg{(}\frac{2I_{RF}}{S}\bigg{)}^{2}\bigg{(}\frac{1}{ T_{S}}\bigg{)}\overline{V_{n,s}^{2}} \tag{18}\]  
\[=\bigg{(}\frac{4I_{RF}}{S\cdot T_{LO}}\bigg{)}\bigg{(}\frac{2I_{RF}}{S\cdot T_ {S}}\bigg{)}4 KT\bigg{(}r_{b2}+\frac{1}{2g_{m2}}\bigg{)} \tag{19}\]  
Substituting the value of \(S\cdot T_{LO}=4\pi V_{LO}\), we obtain the following:  
\[I_{o,n}=\frac{2}{T_{LO}}.2I_{RF}.\frac{V_{n}}{S} \tag{14}\]0  
The output power spectral density depends on LO magnitude (\(V_{\text{LO}}\)) and bias current (\(I_{RF}\)). Indirect switching noise depends on the LO frequency and BJT capacitances existing at the virtual ground.